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Currently in re-write for "2nd Edition".  Unlike most 2nd edition copies, however, which are near replicas of 1st editions,

there are substantial improvements here, including assignments, challenges, etc.

 

 

 

THE PHILOSOPHY BEHIND THE BOOK

Fractals, L-Systems, the Mandelbrot Set, the Logistic Map, Cellular Automata, Sierpinski's Triangle ... the list goes on.    The items, often non-connected and presented as non-related topics, are investigated, modeled, mastered, one after the other.

 

To what end?

 

The image of this view of dynamical systems and mathematical systems education comes to mind:

      

 

 

What's the alternative to presenting materials, ideas, concepts, and concretes as independent and unrelated topics?  Showing the relationship between them all?  Showing the key idea unifying all?  Showing which ideas are more general than other, with some special applications or derivatives of the more general idea?

 

This image comes to mind:

 

 

 

The viability of the computational universe, of course, is the general idea to be communicated in The Proximate Event, and serves as the key idea to be investigated.

 

But how?

 

To the high-school-aged student, uninitiated to the ideas of cellular automata and the plausibility of the computational universe, should the introduction consist of an investigation of the 1-d ECA computational universe?

 

        

 

 

Can the student gain any appreciation for the results of this sampling of the computational universe?  Of the meaning of Rule 30, or Rule 110? 

 

Probably not.

 

But that's the goal.

 

How to get there?

 

What should be the starting point for a student with little background in the ideas of this "New Kind of Order" we're talking about?   What should be the sequence of events be to acquire the interest of the student?

 

Let's compound the equation with a not-so-irrelevant item: because most curriculum are already full, let's not kid ourselves a new topic will be accepted with open arms by teachers.  They have enough to teach already without having something else handed to them. 

 

With this in mind, the ideas we're talking about are to be pursued outside the classroom - by the student learning on their own time!

 

Now the magnitude of our problem becomes clear: how do we get and keep the interest of the introductory student learning on their own time?  Quite a challenge!  In the classroom, we can always fall back onto "because I'm the teacher and you're the student".  Not so when it's the kid at home at night.

 

So what to start with?

 

And not just "what to start with", but additionally, "What is it I want to communicate in this book?"

 

 

 

SOME THOUGHTS

1. the ability to create one's own programs.  The simplest of these ideas still require one to "get in and get their hands dirty"; consequently, one has to be able to program.  Unfortunately, many programming languages have a steep learning curve - clearly a gumption trap for someone who wants to "be up and running quickly".   The intermediate objective:  use Excel as a lever to allow the novice to jump right in.

 

2.  to "jump right in" suggests the student can.  Jumping in without the ability to swim ensures a brutal intellectual drowning.  To avoid this, simple examples must be provided allowing one to go from the easy to the hard.

 

3. points (1) and (2) beg the question, "How best to start?"  Start with an example everybody is familiar with, and allows one to leverage this simple starting point to achieve points (1) and (2).

 

4. the naming of rules is crucial to working with NKS.  The convention is different than what most students are use to.  The simple example should, at some point, start to integrate the model with the naming of the model.

 

5. what specifically regarding the computational universe is sought?  The viability of "rule-based" growth, variation, and the interaction with the environment.  How does one communicate these naturally to the student?  Each chapter starts with a question, answers it, but ends observing some form of anomaly suggesting the theory isn't quite right.  The subsequent chapter addresses the question, and the ideas communicated accordingly.

 

 

 

 

 

THE ULTIMATE GOAL

Demonstrate the viability of the computational universe?  You bet.  Though that was a fundamental issue earlier, what I really want to have happen with this book is NOT the communication of the idea of such a universe.  Rather, it's to get high-school aged students interested in all of this - from different perspectives: biology, chemistry, physics, geology - anything.  One cannot help but look at the universe differently from this new paradigm.

 

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