^10.5 wrapping up
We start off this course with the question
What are Complex Systems?
Our informal lanser ? was there are
large network of simple interacting elements,
which , following simple rules,
produce emergent, collective, complex behavior.
and I told you that this course would provide some
insight into what these all means.
the purpose of this sub-unity ? to go over what we covered-
and see how much insight we gained.
so remember that I mention for Core Disciplines of the Science of Complexity.
for this moment, Dynamics,
Information, Computation,
Evolution/Learning.
and the goals of this course,
were, to give you an overview of what the topics are about,
and to give you a sense of how these topics are integrated in,
to the study of Complex Systems.
and we are doing so to give you a sense of
how we can use idealized models to study these topics.
and we looked at a lot of idealized models,
in Net ? logo.
So if you gotten this far in the course,
you should be very proud of yourself,
because we covered quite a lot and hopefully,
you learn quite a lot about complex systems.
So let's review what we've done,very quickly,
We look at Dynamics and Chaos,
and learn how it can provide a vocabulary.
for describing how Complex Systems change over time.
the vocabulary include ideas, such as
fixed points, periodic attractors, chaos,
sensitive dependence on initial conditions,and other terms.
Dynamics showed us
how Complex behavior can arise from iteration
and iteration of simple rules, such as
bligetics ? map
and we were able to characterize the complexity of behavior,
in terms of the particular kinds of dynamic we saw,
whether they may be fixed points,cycles or chaos,
also the field Dynamics showed a contrast,
between intrinsic unpredictability
which we saw in chaos systems.
and universal properties such as,
the period doubling route chaos, and Figenbaum constants,
our next topic was fractals.
Fractals showed us how a new kind of geometry can be developed.
that characterized in real world patterns,
in a more realistic way than euclidean geometry,
Like Dynamics,
the study of Fractals showed us how complex patterns can arise,
from the iteration of simple rules.
and we were able to characterize complexity,
in a different way here,
in terms of fractals dimension.
information Theory was next and we learn how
Information Theory make analogy between information and physical entropy.
and also a different way of characterizing complexity that is in terms of Information Contents.
so now we see several different ways in which complexity can be characterized.
Genetic Algorithms was next,
that showed us how idealized models of evolution and adaptation can be constructed.
and it also demonstrate how complex behavior
or complex shapes can emerge from the simple rules of evolution.
which themselves can be thought of as iterative,
so you learn automata (tomida),
again we saw, how
so you learn tomida were idealized models of complex systems.
this was another way in which complex patterns emerged from iteration of simple rules.
and we learn about the idea of woofen ？ classes which characterize the complexity of
so you learn tobita behavior,
in terms of these classes of patterns.
We looked at some models of self-organization in biology,
like firefly, synchronization,
bird flocking, fish schooling, ant foraging,
ant task allocation,
and there are many other possible models we didn't cover,
We saw how we can build idealized models such as these
net logo models of self-organizing behavior,
and we may attempt to isolate some of these common principles of these systems,
in terms of dynamics,
the information of the process,
the computation they do, and their adaptation,
With the models of cooperation,
in particularly the Prison's Dilemma model and El Farol Problem model,
this gives us a sense of how idealized model can explain,
self-organized cooperation and social systems,
and in general how idealized models can be used to study for very complex phenomenon.
next we look at networks,
network gives us a vocabulary for describing structure,dynamics of network in real-world
in terms of concepts such as small-world, scale-free,
degree distribution, clustering, path length, etc.
the models that we exploited,
capture some aspects of real world network structure.
such as preferential attachment showed us how we can get scale-free structure in network,
This capture the idea of power load in the degree distribution of networks,
after networks, we cover scaling,
which we looked at some theories of metabolic scaling in biology,
and very Elyria ? of urban scaling.
We saw that looking at how complex systems scale,
as the sizes increase,
Can give clues to be underlined structure and dynamics of the systems,
such as fractal distribution networks.
At the beginning of this course,
I said there were two goals of the Science of Complexity.
The first is
to provide Cross-disciplinary insights into complex systems,
and the second one is
is to develop a general theory of complex systems.
We clearly with manage ? to accomplish the first,
We see a lot of cross-disciplinary insights,
that we get from studying different complex systems,
but in this class we haven't talked about
what is my mean to have a general theory of complex systems.
Many people were asking you,
Can we develop some kind of general unified theory of complex systems?
that is,
Can we develop a mathematical language that is going to unify
the core disciplines of dynamics,
information processing,computation,and evolution in the systems ?
some people has referred to this,
Hypothetical language as
"Calculus of Complexity",
in my book,
Complexity guide tour,
making analogy with some history,
in the late 17 00,
Issac Newton, along with gut free liebies ?,
was developing the calculus,
as James Gleick said in its biography
of Isaac Newton,
He was hampered by the chaos of language,
words still vaguely defined,
and words not quite existing...
Newton believed he could marshal a complete science of motion,
if only he could find the appropriate lexicon...
When I read this,they sounded very much like the state of complexity
systems today,
Newton has a lot of concepts
floating around in the head,
that had been developed by previous narciatations ?,
notions that he was trying to bring together in a unified whole
such as infinitesimal,
derivative, integral, limit,
and he is able, finally,
to unify these different concepts to develop
the preferral lexicon
for understanding motion,
that is , the mathematics that we call calculus.
Well,state of complex systems today,
is very much like the state of mathematics.
back before calculus was invented,
We have all these notions
that seem separate in many ways,
listed a few of them here,
kind of floating work cloud,
and the idea is
that we need to unify them,
someway have mathematics unify all these disciplinary notions,
I am not sure that is going to happen,
It is a very exciting prospect,
but I will leave you with the question
whether complex systems is going to find its own Issac Newton,
either in near or far future perhaps,
To conclude,I will give you a quotation that I like very much,
attributed to Oliver Wendell Holmes,
I do not give a fig for the simplicity on this side of the complexity,
but I would give my life,
for the simplicity, on the other side of the complexity.