Hi, I'm Valerie Bodell. Welcome to Order and Chaos.
This is the first in a series of 3 related courses
in the chaos trilogy. This is a five-week
one credit course. As promised, you don't have to buy any books for this course
and you will not be solving any math or physics problems.
This class is about understanding ideas. Now, there will probably be some unfamiliar
words,
or words used in unfamiliar ways. Don't let these scare you.
Open up a dictionary in your browser as you read. Remember that
educated people look up the meanings of words all their lives
and feel free to collaborate on definitions in D2L.
The syllabus is in D2L and you can read it there in its entirety.
But there are a couple things I wanted to point out in particular. Discussions are
a large part of your grade.
To get full points on the discussions, you need to participate in the conversation,
not just reiterate what your classmates have written. Consider
composing your post and getting things down in your own words
before reading your classmates' posts. I'll be looking for posts of a paragraph
or two
that present your ideas and back them up with examples from the reading.
I'm not worried that you have perfect grammar or spelling.
I'm looking for you to understand the readings; that you can relate them to the
larger world.
Replying with I agree will not be enough.
I'll be looking for replies that comment on what your classmates are discussing
and take it a step further or bring up something new.
My contact information
is in my D2L profile and on the syllabus.
I wanted to make sure you know the best way to contact me is by email.
I generally respond to emails within 24 hours
but I check my email less often on the weekends.
Please do not wait until late Sunday to read your assignment and realize that
you don't know what you're supposed to do.
Please read the assignments early in the week and email me with any questions while I
have time to help you.
If you'd like to talk on the phone, my number is 423
439 7182 and you can leave a message at that number if
I don't happen to be in. If you'd like to meet in person
just give me a call or send me an email and we'll arrange a time to meet.
Your final assignment is a formal paper,
about five pages, about a thousand words. Your paper should have an introduction
with a thesis statement,
a body, a conclusion, and works cited.
Your paper should demonstrate your understanding of dynamical chaotical
systems
by exploring any aspect that interests you. I encourage you to submit a draft
early enough for me to make comments and early enough
for you to make corrections. Now, let's address the question of why anyone would
care about chaos
and how it might help you to know if your system displays chaotic behavior.
The world is full of complex systems,
systems with seemingly random behavior. So let's
start by distinguishing between random and chaotic.
If your system displays chaotic behavior,
then two processes that start from identical
initial conditions always reach the same
end. The process follows regular physical laws,
the current state is a function of the previous state,
and the outcome is predetermined. Chaotic systems
are deterministic but chaotic systems are very sensitive to initial conditions.
So two processes that start from infinitesimally different
initial conditions reach wildly different
ends. This sensitivity to initial conditions
often makes chaotic systems appear random.
To distinguish between the random and chaotic, you would plot points through
time,
a lot of points, and your plot would show that the data points
either cluster into a shape, which we'll discuss in week 3,
or they show a random distribution.
If your system displays random behavior,
then two processes that start from identical
initial conditions may reach different ends
and usually do. The current state is not a function of the previous state
and the outcome does not depend on initial conditions.
Random systems are non-deterministic.
Software engineer, Jason Yin,
has a good discussion of the difference between random and chaotic
and I have included a link on week 1 in D2L,
if anyone is interested. Once we know,
once we can identify a system as one or the other,
as chaotic or random, we can tailor our
reactions to a situation.
Once we understand that weather patterns display
chaotic behavior then we know that we cannot predict
the weather very far into the future because
the remember that the sensitivity to initial conditions
and that our weather system is so complex.
So, remembering that the sensitivity to initial conditions means that
if two processes start from infinitesimally different
initial conditions they go to wildly different
ends. Because our weather system is so complex
we can never identify all of the influences,
all of the variables, and we can never identify them in enough
detail to get our prediction the same as
actual weather because our forecast and the reality
are starting from different initial conditions. They very quickly diverge
toward those wildly different ends. When we study
chaotic systems we will learn that... we will learn to expect
variation but that variation has limits.
So, though the local weather is unpredictable,
it remains within a certain range and that range
shifts predictably and reliably with the seasons.
Because chaotic systems are deterministic
we know that in some situations we can
vary... we can work with variables and try to search for relationships
that lead to stability or appropriate oscillation.
So, we can tailor our reactions to situations
once we know what kind of systems we are dealing with.
Though chaos has negative connotations,
it's not always a bad thing. Granted,
if a bacterial infection is surging out of control
in a body or population, that's probably going to be considered
a bad thing, but understand that reducing chaos
may not always be the goal. There's a value to chaotic processes in the heart
and brain and chaos in the behavior and characteristics
of a natural population preserves adaptability
to a changing natural environment. Chaos in the behavior and characteristics
of a social group preserves adaptability of that group
to a constructed environment, of
big business for example. Understanding chaos
furthers our endeavors in fields as diverse
as industrial engineering technology, disaster management,
cryptography, and population dynamics. As you learn more about chaos
we will look at images of chaos and you may ask
why does seeing a picture of chaos help?
Though chaotic behavior can proceed
from simple mathematical processes, the behavior itself can be very complex
with many variables and instead of dealing with
unwieldy formulas to describe that behavior, chaologists use graphic
representations
and I hope when you look at the images as I can see the order
you'll be able to see it. You will be able to see
stability evolve into chaos and back again
with distinct boundaries between the states. Well, I think that's enough to give you an
idea about chaos
and I look forward to working with you in the next weeks.