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Define,
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Introduction to scientific chaos
Chaos (as science concept)
is "constrained randomness"
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In ordinary conversation "chaos" usually
means "total randomness" or
"unpredictability" |
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However, in math and science "chaos" means
something that LOOKS random or unpredictable but IN REALITY has an
underlying order or pattern to it |
"Chaos theory" began in 1960, with experiments
by (American) Edward Norton Lorenz
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Lorenz
was a meteorologist at MIT (now retired) who
used only a dozen simple equations in a computer to model a very
complex, natural-acting weather system. This led to many
discoveries across science that many "unpredictable" aspects
of nature really do have underlying mathematical principles. |
The best introductory book on chaos is
Chaos:
Making a New Science by James Gleick
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" Where
chaos begins, classical science stops. For as long as the world
has had physicists inquiring into the laws of nature, it has suffered
a special ignorance about disorder in the atmosphere, in the turbulent
sea, in the fluctuations of wildlife populations, in the oscillations
of the heart and the brain.
The irregular side of nature, the discontinuous and erratic
side--these have been puzzles to science, or worse, monstrosities.
But in the 1970s a few scientists in the
United States and Europe began to find a way through disorder.
They were mathematicians, physicists, biologists, chemists, all
seeking connections between different kinds of irregularity.
Physiologists found a surprising order in the chaos that develops in
the human heart, the prime cause of sudden, unexplained death.
Ecologists explored the rise and fall of gypsy moth populations.
Economists dug out old stock price data and tried a new kind of
analysis. The insights that emerged led directly into the
natural world--the shapes of clouds, the paths of lightning, the
microscopic intertwining of blood vessels, the galactic clustering of
stars." |
 Edward Lorenz
(founder of chaos science)
Click to enlarge
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Here's a link to a chaos
site produced by high school students
that really explains it all very
well:
Chaos Site (not required)
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Human
function
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Periodic (rhythmic;
not chaotic) body functions
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Examples of human
functions that vary rhythmically when healthy:
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female reproductive
cycle |
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sleep cycle |
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Aperiodic (nonrhythmic;
chaotic) body functions
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Examples of human
functions that vary nonrhythmically
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heart
rate (HR; beats/min) (NOTE: this is NOT the same as
EKG!!) |
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gait (walking pattern) |
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Change from chaotic to
rhythmic OR change from rhythmic to chaotic
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May be associated with aging,
disease, injury |
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Heart rate (HR) example:
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When healthy, the HR
fluctuates nonrhythmically
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That is, the HR
goes up and down, but relatively unpredictably --you don't
know exactly what your HR will be in the next moment
(even though you may know about what it will be) |
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In aging, injury, and
disease the HR may begin to fluctuate more predictably, going up
and down in a clear, rhythmic pattern
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In this example,
chaotic function is normal and periodic function is abnormal |
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Brain wave
example:
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Brain waves (EEG) fluctuate
chaotically (nonrhythmically) when healthy, even at different
levels of consciousness
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See Chapter 13 for
examples of brain waves (EEG) |
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In a seizure, brain
waves begin to become more rhythmic, less chaotic |
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In this example,
chaotic function is normal and periodic function is abnormal |
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Time ------------------->
A The above an example of chaotic function. It is relatively aperiodic
(without a clear rhythm).
Normal heart rate (plotted in beats/min
across time) should look sort of like this.
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Time ------------------->
B The above is an example of periodic function. It is relatively rhythmic.
A person with a heart rate (beats/min)
that plots out like this is in SERIOUS trouble.
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Click on the photo to enlarge it |
The machine shown in the photograph is used
during labor and delivery and plots the heart rate of the newborn (on
the left side of the graph paper) and plots the relative strength of
uterine (labor) contraction (on the right side of the
graph).
Notice that the baby's HR is a chaotic function (which
is normal) and the mother's uterine contractions are somewhat rhythmic
(which is normal). |
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Human
structure
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Fractal geometry is an
aspect of chaos
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Fractal geometry is
capable of producing highly complex patterns with elements of
unpredictability by using very simple mathematical expressions |
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| Self-similarity is a
characteristic of fractal geometry
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Self-similarity means
that the pattern of each small part of a structure resembles the
pattern of the overall structure
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An example
in nature is found in trees: a pine branch resembles a
whole pine tree, whereas an oak branch resembles a whole oak
tree
pp |
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Other examples in
nature of self-similar structures:
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coastlines |
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plants |
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frost and
snowflakes |
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mineral
crystal formations |
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course of
rivers and streams |
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Another way to see
self-similarity:
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Fractal surfaces
have bumps, each of the bumps have their own bumps, those
bumps have bumps, and so on --nearly infinitely, perhaps
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Each of the
tiniest bumps in such a system "kinda looks
like" any of the largest of the bumps in the same
system |
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Fractal lines have
branches, each branch has branches, each of those branches
have branches, and so on
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Each of the
tiniest branches in such a system "kinda looks
like" any of the largest of the branches in the same
system |
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Many human structures are
self-similar, and therefore are chaotic (at least to some extent)
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Example of structures
in the human body that are self-similar:
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Digestive tract
(intestines, for instance) |
| Blood vessels
(see Fractal Body
- required) |
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Respiratory tract |
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Nerve pathways |
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Self-similarity means
that MANY bumps or branches can fit into a small space
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This makes
absorptive surfaces, as the surfaces in the digestive tract
that absorb nutrients, MORE absorptive than if they were
smooth |
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This makes the
blood vessels capable of carrying more blood to more places
than if it wasn't so highly branched |
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Thus, chaos
improves function by improving structure in the body |
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Human structures are
complex but are built using only a relatively few genes
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Remember, very complex
fractal (chaotic) forms can be be produced with very simple math
expressions
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Thus genetic
information may be simple, but it can produce complex
structure and functions by using chaotic approach |
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The bottom line
What you have to know about chaos for
your course:
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You have to know what the term
chaos (scientific sense)
means in general |
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You have to know that some body functions are
normally chaotic (and
if they become more rhythmic, that's trouble) and examples |
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You have to know that many body structures are
chaotic, exhibiting self-similarity, which increases their
size/complexity (and thus increases the amount/complexity of their
functions) --and know examples |
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This Mini Lesson may be
updated or improved at any time.
Check back frequently or use the
link to the right to inform you of changes. |
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© 1988-April, 2007 Kevin
Patton
ALL rights
reserved
Back
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04/01/07.
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