Curriculum for Cybernetics and Systems Theory

Version 2.0
June 2022

by Alan B. Scrivener

Whole Earth Epilog, 1974

Background

I was first exposed to cybernetics and systems theory as a teenager in the late 1960s, when I read about them in the Whole Earth Catalog, in the first section, entitled "Understanding Whole Systems."

In 1975, at Kresge College, University of California at Santa Cruz, I pursued an individual major in "Whole Systems," sponsored by Gregory Bateson, and taught a one quarter student-directed seminar in "Understanding Whole Systems."

Fifteen years later I was showing the course notes for this class to my teacher friend Jodi Reed, and she asked me how I would do it differently if I did it over. In response I wrote "A Curriculum for Cybernetics and Systems Theory" in 1990 and posted it on the web, with updates in 2002 and 2012. (It wasn't exactly a curriculum, but more of a meandering set of books reviews in the style of the Whole Earth Catalog.)

( people.well.com/user/abs/curriculum.html )

Since then there have been some game-changing developments in these fields, especially how they are taught, and I have also had some time to think about the big picture.

Historical Context

I came to realize that ultimately cybernetics and systems theory represent a trendy repackaging of applied mathematics. Much of our traditional math curriculum is based more on pure mathematics, especially after grade 12, and the problems of training a new generation of mathematicians. Problems are often chosen based on elegance, and on the opportunities to expand the reach of math; proofs are emphasized, since if students are to ultimatly create new math they must use proofs. But the needs of applied math are different; problems are often chosen because of societal needs, even if the exact solutions are provably impossible and approximations are inelegant.

A big game changer has the rise of symbolic solvers, such as MATLAB, Octave and Mathematica (discussed below). They do all of the work except for (1) what we call the word problems, translating the questions into formulas, and then — after the computer solves the equation — (2) validating and applying the solution. With the added benefit of ubiquitous mobile networked computing (smart phones, tablets, and etc.) these solvers are now available for almost any situation.

We need to prepare students for a world in which these trends continue. Certainly it is possible that our technological civilization may collapse; every other one has. But in that case we will put our problems with math education on the back burner for at least a few decades, and have to concentrate on how to eat, which would mean learning to use a 12,000-year-old invention called "the plow." This is vividly illustrated in the first episode ("The Trigger Effect") of James Burke's TV series "Connections" (1978), at about 5:15 - 30:00.

( www.kanopy.com/product/trigger-effect )

But assuming that doesn't happen, we need to stop teaching our students as if the computing resources were unavailable or prohibitively expensive, and instead prepare them for real life in the modern era.

Computer Based Math

Computer Based Math (CBM) illustration

One nation that has done this is Estonia. Regaining independence as a democratic republic in 1991, after life in the Soviet empire and its centralized control, educators there have become independent thinkers and adopted a new curriculum based on the reality of computing in the 21st Century.

( clube.spm.pt/files/estonia-hoim-hommik-kikas-2016-changing-mathematics-education-in-estonia-computer-based-statisti%20(4).pdf )

Conrad Wolfram, brother of Mathematica-founder Stephen Wolfram, has created a new curriculum called Computer Based Math (CBM), which is one of the innovations Estonia has adopted.

( www.computerbasedmath.org/case-for-computer-based-math-education.php )

I don't know many details, but the thinking here seems to run the same way as mine.

Examples First

Education for professional mathematicians almost always proceeds from abstract to concrete:

Consider a function with domain R^2 and range R.

Imagine that for some terrain you have list of latitudes and longitudes with associated altitudes.

Steven Strogatz: In and out of love with math | 3b1b podcast #3 (2021) by Grant Sanderson.

( www.youtube.com/watch?v=SUMLKweFAYk )

I follow that approach in this curriculum.

Assumptions

For simplicity I assume that each course is one hour a day, five days a week. I also assume that the students are, in parallel, taking the standard math curriculum. When I went to grade school in California 50 years ago that sequence was, in middle school (grades 7-8) two years of pre-algebra, and in high school (grades 9-12) one year each of algebra I, geometry, algebra II and pre-calculus. Since then statistics has been added. Typically a college student on a pre-med track will take one year of calculus as their last math course. My course plans assume they have taken these classes in this sequence.

A Note on Books I Haven't Read

I recommend the books I've read. I have vetted them enough to approve them, with whatever caveats I've put in the notes. I mostly selected the books I haven't read by "judging a book by its cover." Think of these books as standing in for whatever titles might deliver on their apparent promises. I will hopefully reduce this list as I revise this document.

...And Heeeere's Johnny!

So here, then, is my latest (work-in-progress) curriculum, designed to be terse and focused on the problem at hand.

	Middle School (grades 7-8)
	I think to many students the math curriculum looks like a long, steep hiking trail up a mountain to a peak permanently obscured by clouds. In my view this impression does them a disservice. They need to know where the trail goes, and also that it branches and isn't just a linear sequence. My goal in the middle school classes is not only to teach them some things they will need — both in life and in later classes in this list — but also to give them an experience in learning math they can fully understand. The courses in probability, symbolic logic (Boolean algebra), game theory and network theory (graph theory) should all be structured so that the material can be verified by inspection or simple calculations. This is not to say that they will be expected to learn everything about these subjects, which can be very extensive and subtle, but that the knowledge presented should be as complete as possible for the classes of problems to be solved, letting them experience being able to completely "wrap their heads around" what is presented.
	probability (one semester) Kids seem to love probability theory because they can use it in games, from Blackjack to Dungeons and Dragons. Be wary of parents objecting if you teach them casino games — maybe use permission slips — but I have found that an understanding of the subject discourages gambling. A goal of this class would be to learn to figure odds using Markov trees and combinatorial functions.
1.	Book Title Mathematics: A Human Endeavor Author Jacobs, Harold R. Date 1970 Grades 7-10 Keywords SYMBOLIC MATH PROBABILITY THEORY	Notes This award wining text covers more than is needed in this class, and also seems very good at helping get kids interested in math.
2.	Book Title The Black Swan Author Taleb, Nassim Nicholas Date 2007 Grades 7-16 Keywords PROBABILITY THEORY	Notes Taleb's writing helps balance out the false feeling that probability theory can be used everywhere; he points out the difficulty of figuring odds for rare events.
3.	Book Title Probability, Decisions and Games: A Gentle Introduction using R Author Rodríguez & Mendes Date 2018 Grades 7-16 Keywords PROBABILITY THEORY	Notes This looks like a fun way to have the students do numerical experiments with probability. [I have not read this book.]
4.	Software Title R From The R Project Grades 9-20 Keywords STATISTICS, PROBABILITY	Notes This is the software you'll need to use the above book. Available from the R Project web site. ( www.r-project.org )
	symbolic logic (Boolean algebra) (one semester) A nice thing about symbolic logic is that in most cases you can come to definitive answers just by looking at all possible combinations, since each variable can only have one of two values (1 or 0, True or False). I would caution to avoid getting "wrapped around the axle" on the meaning of "IF A THEN B" which has more meanings in English than in symbolic logic, especially when time is involved. I prefer "A IMPLIES B" or "A -> B" instead.
5.	Book Title Boolean Algebra Is for Children Author Romero, Julio César Martínez Date 2017 Grades 7-16 Keywords SYMBOLIC MATH BOOLEAN ALGEBRA	Notes [I have not read this book.]
6.	Book Title The Lady or the Tiger? & Other Logic Puzzles Author Smullyan, Raymond Date 1982 Grades 7-16 Keywords LOGIC PUZZLES	Notes Kids often love puzzles and games. One way to use this book is to present a puzzle a day to solve and discuss. Also give students extra credit for bringing in interesting logic puzzles and games.
7.	Book Title The CMOS Cookbook Author Lancaster, Don Date 1997 Grades 7-16 Keywords DIGITAL LOGIC BOOLEAN ALGEBRA	Notes Get a breadboard (reconfigurable circuit board) with power supply and some logic chips (5 volt CMOS), along with some switches for input and LEDs for output, and have the kids play around with them. It makes this stuff far more concrete.
8.	Movie Title A Computer Glossary Directed By Charles and Ray Eames Date 1968 Grades 13-16 Keywords LOGIC CIRCUITS	Notes This cute video was produced by the Eames for an IBM exhibit over fifty years ago, dealing with what we now call mainframe computers, many technical generations ago, and yet it is still useful for its cartoon illustrations of logic gates. Show it at the first class meeting. ( www.youtube.com/watch?v=eIgX6sPOqCY )
	game theory (one semester) It's easy to get kids interested in a class called "game theory," for obvious reasons. The goal of this class should be for them to be able to analyze two-person strategy games and to understand concepts like best strategy and Nash equilibrium.
9.	Book Title Game Theory 101: The Complete Textbook Author Spaniel, William Date 2011 Grades 13-16 Keywords GAME THEORY	Notes [I have not read this book.]
10.	Book Title Gladiators, Pirates and Games of Trust: How Game Theory, Strategy and Probability Rule Our Lives Author Shapira, Haim Date 2017 Grades 13-16 Keywords GAME THEORY	Notes [I have not read this book.]
11.	Game Bridge-It Date 1960 Grades 13-16 Keywords GAME THEORY	Notes It would be a bait-and-switch to offer middle schoolers a game theory class and then not let them play games. I list Bridge-It here, a commercialized version of the Shannon Switching Game created by Claude Shannon, inventor of the bit. I don't think it's being made any more but you can find units on eBay. Other games I'd suggest: The Game of Pure Strategy — also known as Goofspiel The Foxhole Game — taught at the Army War College; described by Martin Gardner in "Mathematical Magic Show" (1965), chapter three. ( www.amazon.com/exec/obidos/ASIN/0394726235/hip-20 ) Hex aka John — played on a hexagonal grid, co-invented by John Nash 4D Tic-Tac-Toe use 16 4x4 grids Nim Go Maelstrom — like chess but with pieces on every space at the start Nomic — a game in which players change the rules Play tournaments, perhaps every Friday, and give extra credit for briging in interesting games. They will soon learn that some games are hard to analyze using classic game theory.
	network theory (graph theory) (one semester) I prefer to call this field "network theory" because the name "graph theory" is so vague and misleading. Sometimes I call it dots connected with lines. It is a new field; when I studied it in college there were no texts. I still haven't found a great one. But there are some good videos out there. The goal of this course should be to introduce the concepts (probably by using Euler's famous Seven Bridges of Königsberg problem), the terminology (including walks and trees) and to show the mapping of a graph onto a binary matrix, along with the shortcuts this allows.
12.	Video Title Graph Theory: 57. Planar Graphs Author Sarada Herke Date 2015 Grades 7-20 Keywords GRAPH (NETWORK) THEORY PLANAR GRAPHS	Notes This whole series is pretty good by I especially like the episode on planar graphs. ( www.youtube.com/watch?v=wnYtITkWAYA )
13.	Book Title Introductory Graph Theory Author Chartrand, Gary Date 1985 Grades 7-16 Keywords SYMBOLIC MATH GRAPH (NETWORK) THEORY	Notes This book will do OK, but it's a bit "mathy." It suffers from introducing symbols before examples. This can be fixed in lectures, by presenting examples first before each set of definitions.
14.	Book Title Six Degrees: The Science of a Connected Age Author Watts, Duncan J. Date 2003 Grades 7-16 Keywords GRAPH (NETWORK) THEORY	Notes This book details the ways graph theory is relevant to the age of internet and social media.
15.	Book Title Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives — How Your Friends' Friends' Friends Affect Everything You Feel, Think, and Do Author Christakis, Nicholas A. Date 2011 Grades 7-16 Keywords GRAPH (NETWORK) THEORY	Notes This book is more rigorous than "Six Degrees..." Christakis is at the forefront of social network research today, and explains it well.
16.	Book Title Social Network Analysis for Startups Author Tsvetovat & Kouznetsov Date 2003 Grades 11-20 Keywords COMPUTER PROGRAMMING GRAPH (NETWORK) THEORY	Notes This book is really too advanced for this grade level, with the programming skills needed, but if you skip that stuff the concepts are incredibly useful, especially the "grey cardinal." If you have students who want to tackle the programming for extra credit, do encourage them.
17.	Video Title Why this puzzle is impossible Author Grant Sanderson, 2Blue1Brown Date 2021 Grades 7-20 Keywords GRAPH (NETWORK) THEORY	Notes Show this video after you have the students attempt the "three houses and three utilities" puzzle. Also expose the to other puzzles, like the six party guests in Ramsey Theory. Give extra credit for students bringing in other puzzles based on graph theory. ( www.youtube.com/watch?v=VvCytJvd4H0 )
18.	Video Title N is a number, A portrait of Paul Erdös Director George Paul Csicsery Date 1993 Grades 7-20 Keywords GRAPH (NETWORK) THEORY	Notes This documentary huamnizes graph theory by profiling a beloved practitioner. The concept of "Erdös Number" is useful, as well as the related "Kevin Bacon number." ( www.youtube.com/watch?v=djQkj4SaUYs )
	High School (grades 9-12)
	cybernetics and systems theory I (one semester) I think this class is the most important of the bunch. I've listed too many books, but the approach I recommend is to work through Ashby and Abraham & Shaw together, make Gleick required reading and let let them pick one other.
19.	Movie Title Powers of Ten Directed By Charles and Ray Eames Date 1977 Grades 7-16 Keywords THE UNIVERSE	Notes Show this video at the first class meeting to communicate the sweep of the subject matter.
20.	Book Title The Information: A History, a Theory, a Flood Author Gleick, James Date 2011 Grades 7-14 Keywords INFORMATION THEORY	Notes This book does a great job of describing the paradigm shifts civilization has gone through in the information age.
21.	Book Title An Introduction to General Systems Thinking Author Weinberg, Gerals M. Date 1975 Grades 7-16 Keywords SYSTEMS THINKING	Notes A nice non-math introduction to the subject.
22.	Book Title Systemantics: How Systems Work and Especially How They Fail Author Gall, John Date 1977 Grades 7-16 Keywords HUMOR SYSTEMS THINKING	Notes A hilarious lampoon that also is full of truths.
23.	Paper Title Cybernetic Explanation Author Bateson, Gregory Date 1967 Grades 7-16 Keywords CYBERNETICS	Notes Have them read this essay the first week, and discuss.
24.	Book Title An Introduction to Cybernetics Author Ashby, W. Ross Date 1956 Grades 7-16	Notes Thus classic work is still a great text.
25.	Book Title Dynamics: The Geometry of Behavior — Part One: Periodic Behavior Author Abraham & Shaw Date 1982 Grades 7-16 Keywords LIGHT SYMBOLIC MATH SYSTEMS THEORY	Notes Ashby deals entirely with finite state systems. This book introduces the continuous case. Too bad there are no problems assigned.
26.	Software Title Colossal Cave Adventure From Grades 7-20 Keywords FINITE STATE MACHINE WITH INPUT	Notes Have the students play this game, which is mostly a finite state machine with inputs. Have them draw a map for extra credit. ( en.wikipedia.org/wiki/Colossal_Cave_Adventure )
	cybernetics and systems theory II (one semester) This class continues the exploration of continuous systems. Work through Meadows and Abraham & Shaw over the semester, and let the "Chaos..." reading inspire discussions of periodic vs. chaotic attractors.
27.	Book Title Thinking In Systems Author Meadows, Donella Date 2008 Grades 7-16 Keywords LIGHT SYMBOLIC MATH SYSTEMS THINKING	Notes Meadows was a student and collaborator of Jay Forrester, and worked on the "Limits to Growth" study. This book is an extremely accessible introduction to systems modeling, low on math but high on rigor.
28.	Book Title Chaos: Making a New Science Author Gleick, James Date 1987 Grades 9-20 Keywords SYSTEMS THEORY NON-LINEAR SYSTEMS CHAOS	Notes A well told layperson's introduction to the birth of chaos theory in the 1980s.
29.	Video Title This equation will change how you see the world (the logistic map) Contributors Veritasium Date 2020 Grades 19-20 Keywords CHAOS	Notes Watch this video while reading "Chaos..." ( www.youtube.com/watch?v=ovJcsL7vyrk )
30.	Book Title Dynamics: The Geometry of Behavior — Part Two: Chaotic Behavior Author Abraham & Shaw Date 1982 Grades 7-16 Keywords LIGHT SYMBOLIC MATH SYSTEMS THEORY	Notes A wonderful menagerie of chaotic attractors.
31.	Software Title Stella From ISEE Systems Grades 7-20 Keywords VISUAL MODELING VISUAL PROGRAMMING DYNAMICAL SYSTEMS ORDINARY DIFFERENTIAL EQUATIONS	Notes This is an expensive software package but schools get a break and hopefully can reuse it with many students. It allows them to visually build systems models like those in Meadows. ( www.iseesystems.com/store/products/stella-architect.aspx )
32.	Movie Title Hidden Figures Directed By Theodore Melfi Date 2016 Grades 7-16 Keywords EULER'S METHOD	Notes Based on the true story of mathematician Katherine Johnson and her team's contributions to the Apollo moon shot.
	cybernetics and systems theory III (one semester) In this semester the students learn more about how to analyze chaotic and other systems, and more real world examples.
33.	Book Title Dynamics: The Geometry of Behavior — Part Three: Global Behavior Author Abraham & Shaw Date 1982 Grades 7-16 Keywords LIGHT SYMBOLIC MATH SYSTEMS THEORY	Notes Continuing the cartoon version of systems theory. Work through this text over the semester.
34.	Book Title Complexity: The Emerging Science at the Edge of Order and Chaos Author Waldrop, M. Mitchell Date 1992 Grades 13-20 Keywords SYSTEMS THEORY NON-LINEAR SYSTEMS CHAOS	Notes A tale of real world problems bedeviled by simplistic models.
35.	Book Title Moneyball: The Art of Winning An Unfair Game Author Lewis, Michael Date 2004 Grades 7-16 Keywords DATA ANALYTICS	Notes One of the hardest tasks in modeling a system is choosing the right variables. Think of this as a baseball case study of identifying correct variables.
36.	Book Title A First Course in Mathematical Modeling Author Giordano, Fox & Horton Date 2013 Grades 11-16 Keywords COMPUTER PROGRAMMING SIMULATION	Notes Use this text to have the students create their own models of real world systems. [I have not read this book.]
37.	Book Title II Cybernetic Frontiers: Both Sides of the Necessary Paradox (Conversations with Gregory Bateson) & Fanatic Life and Symbolic Death Among the Computer Bums Author Brand, Stewart Date 1974 Grades 7-20 Keywords CYBERNETICS, SPACEWAR, BATESON	Notes This serves as a preview to entice students to take the Bateson class (below). Online text available. ( archive.org/stream/iicyberneticfront00bran/iicyberneticfront00bran_djvu.txt )
38.	Software Title Spacewar Author Russell, Graetz, Wiitanen, Saunders, Piner, et. al. Date 1962 Grades 7-20 Keywords HUMAN IN THE LOOP	Notes Since the Brand book also discusses Spacewar, an early computer game that explored humans and computers in tight feedback loops (and paved the way for a huge industry) , you have to let them play the game. ( spacewar.oversigma.com )
39.	Book Title I Seem to Be a Verb Author Fuller, Buckminster, Agel, Jerome and Fiore, Quenton Date 1970 Grades 7-20 Keywords SYNERGETICS	Notes This serves as a preview to entice students to take the Fuller class (below).c [There may be an availability problem with this book -- it originally had a 65 cent (US) cover price and sold used for a quarter; now it's nearly $1000 on Amazon Markets. If necessary substitute "Operating Manual for Spaceship Earth.]
	calculus for systems theory I & II (two semesters) I once bragged that I could teach middle schoolers calculus if I could leave out limits and proofs. In my eZine, "Cybernetics in the Third Millennium (C3M)" I described how my daughter called my bluff at age 16 and I gave a calculus summer school. Teaching Calculus to a Sixteen-Year-Old (2012) by Alan Scrivener ( people.well.com/user/abs/Cyb/archive/c3m_1003.html#sec_1 ) This course is based on that experiment.
40.	Video Title Why don't they teach Newton's calculus of 'What comes next?' Contributors Mathologer Date 2021 Grades 11-20 Keywords FINITE CALCULUS	Notes This video explains a simple method developed by Newton for doing finite calculus, and introduces key calculus concepts in an understandable way. It is also the technique used by the famous gear computer of Charles Babbage, the Difference Engine. ( www.youtube.com/watch?v=4AuV93LOPcE )
41.	Book Title Professor E. McSquared's Original, Fantastic and Highly Edifying Calculus Primer Author Swann & Johnson Date 1975 Grades 11=14 Keywords SYMBOLIC MATH	Notes This charming text in comic book form represents functions as cute robots that take in and dispense numbers, and covers the material in first semester college calculus, with problems.
42.	Book Title Mechanical Universe Author Goodstein, David L. Date 1986 Grades 11-14 Keywords SYMBOLIC MATH	Notes This text partially overlaps with the excellent video series of the same name. It teaches calculus for physics, which is an excellent way to learn.
43.	Video Title Mechanical Universe Contributors Goodstein, Dr. David, Blinn, Jim, Buffa, Peter F., Rothschild, Mark Date 1985 Grades 11-20 Keywords MECHANICS, CALCULUS	Notes Watch an episode a week and discuss.
44.	Software Title Wolfram Alpha From Grades 7-20 Keywords SYMBOLIC SOLVER	Notes This tool is available as a web page or smart phone app, and can solve every symbolic calculus problem I have thrown at it. ( www.wolframalpha.com )
45.	Book Title Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Author Strogatz, Steven H. Date 2014 Grades 9-16 Keywords SYMBOLIC MATH	Notes Because several generationS of mathematicians and engineers studied linear systems and developed poor intuitions for the real world (like denying the exist of rogue waves on the ocean), I thinks it's important for students to study nonlinear systems first, and get to the admittedly beautiful linear theory later if ever. [I have not read this book.]
	systems theory for life sciences (one semester) For hundreds of years people have been building mathematical models of physical systems, with good results, using concepts such as mass, velocity, momentum and energy. But applying these same concepts to biological systems has not been as fruitful. The discovery of chaos in the 1980s brought a new set of tools for life sciences, and this course is designed to teach how to use them. Clearly there are too many books listed. Use Garfinkel, Shevtsov & Guo as the main text and have students each pick one other book from Kelly, Dawkins, Ridley and Levy.
46.	Paper Title A mathematics for physiology Author Garfinkel, Alan Date 1983 Grades 11-20 Keywords CYBERNETICS	Notes This seminal paper from Dr. Garfinkel gives a brief history of systems theory from Newton to the post-chaos era and illustrates why it is so useful for life sciences. It also contains what I call "Garfinkel's Law," the idea that the sophistication of a scientific specialty and its models can be roughly measured by the complexity of the model's attractors (point, loop, strange attractor). ( ajpregu.physiology.org/content/245/4/R455.abstract ) ( www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=6624944&dopt=Abstract )
47.	Book Title Modeling Life: The Mathematics of Biological Systems Author Garfinkel, Shevtsov & Guo Date 2017 Grades 9-16 Keywords SYMBOLIC MATH LIFE SCIENCES	Notes Over a decade ago I concluded that the pre-med college curriculum was flawed. It generally requires one year of college calculus. Doctors I know have said this was pretty useless. Meanwhile the math majors get more advanced calculus classes until they reach linear algebra in the third year, which is an introduction to systems theory and Ordinary Differential Equations (ODEs). This is the class I thought would be useful to medical students. I figured if you took out the proofs and added computer assistance, you could cover much of his material in the first year. Well, in 2021 I found out that Dr. Alan Garfinkel at UCLA (who I met in the 1990s) had been thinking along similar lines. In this text he and his team present the systems theory they deem useful to physicians, and they go one further by dealing with nonlinear systems. Their most laudable effort though went into getting a number of medical schools to accept this class instead of a year of calculus. [I have not read this book.]
48.	Video Title Mathematics for Life Sciences - Garfinkel Lectures Contributors Garfinkel, Alan Date 2020 Grades 13-20 Keywords NONLINEAR SYSTEMS	Notes This series covers some of the material in Garfinkel, Shevtsov & Guo's text. ( www.youtube.com/playlist?list=PLGSoFisPnIYoEWxs9jA88dQ9vPPpE4gk2 )
49.	Book Title Out of Control: The New Biology of Machines, Social Systems, and the Economic World Author Kelly, Kevin Date 1992 Grades 7-16 Keywords LIFE SCIENCES	Notes A science journalist and Whole Earth Review contributor's tangled tale of our recent realizations of how unmanageable life is.
50.	Book Title The Selfish Gene Author Dawkins, Richard Date 1976 Grades 7-16 Keywords LIFE SCIENCES	Notes Some reviewers have said this book focuses too much on competition at the expense of cooperation, but I think it is a very rigorous look at how genes become more adaptive. It also contains the first use of the word "meme," coined by Dawkins.
51.	Book Title Genome: The Autobiography of a Species in 23 Chapters Author Ridley, Matt Date 2006 Grades 7-16 Keywords LIFE SCIENCES	Notes This is a twenty year old snapshot of our understanding of the human genome. Perhaps a better book is out now.
52.	Book Title Artificial Life: The Quest for a New Creation Author Levy, Steven Date 1992 Grades 9-16 Keywords LIFE SCIENCES	Notes Some mysteries of life and evolution can be illuminated through simulations.
53.	Software Title Predator, Prey, Poison From NetLogo Grades 7-20 Keywords CHAOS IN POPULATION MODELS	Notes This game allows student to play with predator/prey models and observe the sometimes chaotic results. ( ccl.northwestern.edu/netlogo/models/community/Predator,%20Prey,%20Poison )
54.	Book Title A Kid's Guide to Making a Terrarium Author Bearce, Stephanie Date 2009 Grades 9-16 Keywords LIFE SCIENCES	Notes Bateson used to complain about the arrogance of believing your own theories, and as an antidote recommended exposing your mind to more "natural history," the real behavior of real living things. Have the students raise some critters.
55.	Paper Title On Empty-Headedness Among Biologists and State Boards of Education Author Bateson, Gregory Date 1970 Grades 7-16 Keywords EVOLUTION	Notes In this contrarian essay, Bateson argues against banning religious creation stories from biology classes. He essentially says that though their answers may be wrong or even nonsensical, the questions they ask are profound, often better than those asked by evolutionists.
	finite systems (one semester) I guess if you believe the quantum physicists that there is a low limit to the sizes of space and time intervals (Planck limits) then all systems are finite, but we still use math tools that assume continuous functions and infinities. This class is an opportunity to explore simple systems that have complex behaviors.
56.	Book Title Godel, Escher, Bach: an Eternal Golden Braid Author Hofstadter, Douglas R. Date 1979 Grades 9-16 Keywords CONSCIOUSNESS	Notes Hofstadter shows how some very simple finite systems can quickly get bound up in paradoxes, building towards an intuitive understanding of Godel's Incompleteness Theorem.
57.	Book Title The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge Author Poundstone, William Date 1985 Grades 11-16 Keywords CELLULAR AUTOMATA	Notes Before Wolfram, this book pointed the way towards using cellular automata to understand emergent properties of systems.
58.	Book Title A New Kind of Science Author Wolfram, Stephen Date 2002 Grades 7-16 Keywords CELLULAR AUTOMATA	Notes When Wolfram published this book he got a lot of blowback, mostly for bragging I think, but I thought he was definitely onto something. I use the term "Wolfram's Method" for his technique of looking at — or trying to look at — all possible outcomes of a defined system. I have used the method to study Boolean Algebra (symbolic logic) and finite state machines. This book applies the method to cellular automata, Turing machines and other models. The notes are a good source of extra credit projects.
59.	Paper Title Steps to an ecology of emergence Authors Malloy, T. E., Bostic St Clair, C. & Grinder, J. Date 2005 Grades 09-20 Keywords HIERARCHY, SELF ORGANIZING SYSTEMS	Notes This paper appeared in a special edition of "Cybernetics & Human Knowing: A Journal of Second-Order Cybernetics Auto Poiesis and Cyber-Semiotics" (v. 11, n. 3) devoted to "Gregory Bateson -- essays for an ecology of ideas." Without saying so, it applies Wolfram's method to self-organizing hierarchical systems, with delightful results. ( www.amazon.com/exec/obidos/ASIN/1845400321/hip-20 ) ( citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.694.1199&rep=rep1&type=pdf )
60.	Software Title Conway's Life Author John Horton Conway, et. al. Date 1970 Grades 7-20 Keywords CELLULAR AUTOMATA	Notes You gotta let the students play with Conway's "Life" game. ( playgameoflife.com )
	machine learning (one semester) I'm not going to call this class "artificial intelligence" because I think we are a long way off from there. But we can get software to learn, which we confusingly call "machine learning." A lot of what is written on this topic is gibberish by people who are not practitioners, so I think it's important to have students actually program the software. For starters have the students build and play with a "MENACE" machine, which is literally a cardboard and beads computer that learns to play tic-tac-toe. MENACE (Matchbox Educable Naughts and Crosses Engine) is the invention of Donald Michie, a biologist at the University of Edinburgh. He first described the machine in 'Trial and Error', in Penguin Science Survey 1961, Vol. 2. It clearly illustrates some simple concepts in machine learning. It is tersely but adequately described in a short post: Menace: A simple tic tac toe learning computer constructed out of just 300 matchboxes and colored beads. (2003) by Joth ( everything2.com/user/Joth/writeups/Menace ) The Hofstadter book describes a project to program a word scramble solver that makes mistakes similar to human ones.
61.	Book Title Fluid Concepts and Creative Analogies: Computer Models Of The Fundamental Mechanisms Of Thought Author Hofstadter, Douglas R. Date 1996 Grades 9-16 Keywords MACHINE LEARNING	Notes Work through this text as a sideline through the semester.
62.	Book Title Introduction to Machine Learning with Python: Guide for Data Scientists Author Muller & Guido Date 2003 Grades 11-20 Keywords COMPUTER PROGRAMMING MACHINE LEARNING	Notes Use this or another text to explore writing machine learning software. [I have not read this book.]
63.	Software Title Python Author Guido van Rossum Date 1991 Grades 8-20 Keywords INTERACTIVE PROGRAMMING	Notes Python is a popular, powerful language that is easy to get started with, and has an interactive mode for exploring. There is also an active and helpful online community. ( www.python.org )
64.	Toy LEGO Mindstorms NXT 2.0 Date 2009 Grades 7-12 Keywords ROBOTICS	Notes For a change of pace, let the students build and program robots. (You may want to get a more recent version of LEGO Mindstorms.)
	systems for business (one semester) In the two decades that I've been writing my eZine C3M (op. cit.) the most requested subject for me to address has been applying cybernetics and systems theory to business. For many this points directly to the work of Stafford Beer, author of "Brain of the Firm" among many others, and a pioneer of operations research and management cybernetics. But I dunno, maybe it's me but I've read some of his stuff and didn't get many takeaways. So instead I have focused on some early work by Forrester, a recent guide to business analytics for the lay person, and a recent text in use at University of California at San Diego (UCSD). But first have the students pick either large or small businesses, and read either Peters & Waterman or Gerber. These books contain no cybernetics or systems theory (overtly), but deal with the human elements in management. They are emphatic reminders that there is art as well as science in operating a business.
65.	Book Title In Search of Excellence: Lessons from America's Best-Run Companies Authors Peters, Thomas J. Peters, Waterman, Robert H. Jr. Date 1982 Grades 11-16 Keywords LARGE BUSINESS MANAGEMENT	Notes Bravely looks as the paradoxes of great companies, such as "simultaneous loose-tight properties."
66.	Book Title The E-Myth Revisited: Why Most Small Businesses Don't Work and What to Do About It Author Gerber, Michael E. Date 1985 Grades 09-16 Keywords SMALL BUSINESS MANAGEMENT	Notes The "E-Myth" (entrepeneur myth) is that you can turn your hobby into a business and it will be smooth sailing. This book is a guide to weathering the storms.
67.	Book Title Industrial Dynamics Author Forrester, Jay W. Date 1985 Grades 9-20 Keywords MANAGEMENT SIMULATION	Notes Back when computers were obscenely expensive Jay Forrester at the Massachusetts Institute of Technology (MIT) got funded to simulate business processes, and kicked off a revolution of better understanding business dynamics. Much of this book deals with inventory and shipping delays, which can be very unintuitive. [I have not finished this book.]
68.	Book Title Keeping Up with the Quants: Your Guide to Understanding and Using Analytics Author Davenport & Kim Date 2013 Grades 11-16 Keywords SYMBOLIC MATH	Notes This not a text on how to become a "quant" (quantitative business analysts), though it might not be a bad place start. As the saying goes, "You can't manage what you can't measure." This book helps business people begin collecting the kind of data the quants will find useful. [I have not finished this book.]
69.	Book Title Introduction to Operations Research Author Hillier, Frederick Date 2014 Grades 11-16 Keywords SYMBOLIC MATH	Notes Operations research, also known as management science, is a grab bag of rigorous techniques developed by scientists to solve problems in logistics and other business challenges. [I have not finished this book.]
	special seminar: the Pattern Which Connects of Gregory Bateson (one semester) Bateson began his career as an anthropologist, but after participating in the Macy Foundation meetings at which cybernetics was born he began to move from field to field bringing clarity: psychiatry, ecology, biology, ethology (animal behavior), art, religion and epistemolgy (how we know what we know), bringing a cybernetic sensibility to each. He was my mentor at Kresge College, University of California at Santa Cruz (UCSC).
70.	Book Title Mind and Nature, A Necessary Unity Author Bateson, Gregory Date 1979 Grades 7-20 Keywords SYSTEMS THINKING LIFE SCIENCES	Notes Bateson's most accessible book, the only one he wrote for the general public.
71.	Book Title Steps to an Ecology of Mind Author Bateson, Gregory Date 1972 Grades 9-20 Keywords CYBERNETICS MENTAL SYSTEMS	Notes This collection of papers, essays and talks by Bateson span most of his career. The received wisdom is to read the Metalogues, and then read the book backwards, section by section.
72.	Book Title Our Own Metaphor: A Personal Account of a Conference on the Effects of Conscious Purpose on Human Adaptation Author Bateson, Mary Catherine Date 1972 Grades 9-20 Keywords CYBERNETICS MENTAL SYSTEMS CONSCIOUSNESS	Notes Most of the important conversations at a seminar happen during session breaks, and are usually not transcribed. Bateson's daughter Mary Catherine paid attention during her father's conference on "The Effects of Conscious Purpose on Human Adaptation" and recorded a lot of good stuff. Both the ideas and the interactions are valuable.
	special seminar: the Synergetics of Bucky Fuller (one semester) If not on an intellectual island, Fuller certainly was on his own peninsula of systems theory, and his work doesn't connect much to others, but he was such a profound thinker he is worth studying.
73.	Book Title Critical Path Author Fuller, R. Buckminster & Kuromiya, Kiyoshi Date 1978 Grades 9-20 Keywords SYNERGETICS	Notes In my opinion the best, clearest statement of Fuller's ideas in his writings.
74.	Book Title A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller Author Edmondson, Amy Date 1987 Grades 7-20 Keywords SYNERGETICS	Notes Edmondson worked for Fuller at the end of his life, and after he was gone wrote this book to explain his geometric ideas in plain English.
75.	Book Title Bucky Works: Buckminster Fuller's Ideas for Today Author Baldwin, J. Date 1996 Grades 7-20 Keywords SYNERGETICS	Notes Baldwin is a tinkerer who has played woth many of Fuller's designs, and talks about the nuts and bolts of his inventions.
76.	Book Title Buckminster Fuller: Starting with the Universe (Whitney Museum of American Art Book) Author Hays, Miller, Picon, Smith & Tomkins Date 2008 Grades 7-20 Keywords SYNERGETICS	Notes Many architects denied Fuller was one of them; same with many engineers. But artists seemed to embrace him as one of their own. This view from the Whitney Museum of American Art emphasizes that aspect of his work.
77.	Toy Flexistix STEM Building Geodesic Structures, Featuring 177 Multi-Colored Bamboo Pieces From Hape Date 2018 Grades 7-20 Keywords GEODESICS	Notes You can't talk about geodesics without playing with the shapes. This is one of many kits available. You can also build octet trusses out of toothpicks and miniature marshmallows. You probably should begin the class by having the students build the 5 Platonic solids out of toothpicks and miniature marshmallows, and note that only the 3 made of triangles are stable.
	University Undergraduate (grades 13-16)
	advanced topics in systems theory I & II (two semesters) This is a class to explore Partial Differential Equations (PDE) in the context of systems theory. The above illustration shows sand on cymbals, making shapes predicted by PDEs.
78.	Book Title Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineering Applications Author Vande Wouwer, Alain, Saucez, Philippe, & Vilas Fernandez, Carlos Date 2014 Grades 13-20 Keywords COMPUTER PROGRAMMING SIMULATION DIFFERENTIAL EQUATIONS	Notes Instructions on how to model systems and play with the models in Matlab and similar packages. [I have not read this book.]
79.	Software Title MATLAB From Mathworks Grades 9-20 Keywords SYMBOLIC SOLVER	Notes The acclaimed Matlab software — pricey but there are educational discounts. ( www.mathworks.com/products/matlab.html )
80.	Software Title Octave From Mathworks Grades 9-20 Keywords SYMBOLIC SOLVER	Notes A similar package to Matlab available for free. ( www.gnu.org/software/octave/index )
81.	Book Title Dynamics: The Geometry of Behavior (Vols. 1-4) Author Abraham & Shaw Date 1982 Grades 13-20 Keywords NON-LINEAR SYSTEMS CHAOS	Notes These volumes are listed for various classes above, but the idea here os to go back through them building models of each example and playing with them.
	advanced linear systems I & II (two semesters) In the old days when few nonlinear systems were understood, both mathematicians end engineers were taught the linear theories and so generations developed false intuitions. This lead to errors in bridge design, understanding water waves, and even economic decisions. For this reason I advocate for teaching nonlinear techniques first, kludgy though they are. But the linear systems theory is one of the most beautiful in all of mathematics, and it is useful in some cases. This course explores it at length.
82.	Video Title Essence of linear algebra [16 videos] Contributors 3Blue1Brown — Sanderson, Grant Date 2021 Grades 11-20 Keywords LINEAR ALGEBRA	Notes Great visual explanations of linear algebra concepts. Work through them over the semester. ( www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab )
83.	Book Title The Manga Guide to Linear Algebra Author Shin & Iroha Date 2012 Grades 13-20 Keywords SYMBOLIC MATH	Notes A delightful translation of a Japanese comic about love and math.
84.	Book Title Control System Design: An Introduction to State-Space Methods Author Friedland, Bernard Date 1986 Grades 11-20 Keywords SYMBOLIC MATH CONTROL THEORY	Notes Perhaps the most successful application of linear systems theory is in orbital dynamics which got us to the moon. This text clearly introduces the concepts, and also shows how to use flow diagrams to describe control systems.
85.	Book Title Mathematica: A Handbook for Precalculus, Calculus and Linear Algebra Author Torrence, Eve Date 2009 Grades 13-20 Keywords SYMBOLIC MATH DIFFERENTIAL EQUATIONS LINEAR SYSTEMS	Notes Instructions on how to use the Mathematica package to model linear systems. [I have not finished this book.]
86.	Software Title Wolfram Mathematica From Grades 13-20 Keywords SYMBOLIC SOLVER	Notes Powerful but pricey package. Look for educational discounts. ( www.wolfram.com/mathematica )
	special seminar: the roots of cybernetics and systems theory (one semester) I came at cybernetics from the historical direction, so this material is beloved to me, but it doesn't fit into the above curriculum very well, so I've assembled it here. Again there are too many books. The ones with a keyword HISTORY are after-the-fact accounts. The last 6 books are original works of relevance. Have the students divide up the books and give book reports to the class.
87.	Paper Title Feedback Control: An Invisible Thread in the History of Technology Author Bernstein, Dennis S. Date 2002 Grades 9-20 Keywords FEEDBACK HISTORY	Notes An informative essay. ( www-personal.umich.edu/~dsbaero/editorials/2002-InvisibleThread.pdf )
88.	Paper Title An historical essay on cybernetics Author Asaro, Peter Date 2021? Grades 11-20 Keywords CYBERNETICS HISTORY	Notes An informative essay. ( cybsoc.org/?p=1549 )
89.	Video Title High Tech Heroes, #10, part 1: Heinz von Foerster and Cybernetics Contributors atwaterpub Date 2016 Grades 09-20 Keywords HISTORY OF CYBERNETICS	Notes Von Foerster is always a joy to listen to. He was one of the pioneers at the Macy meetings. ( www.youtube.com/watch?v=GWcyHbmsXS0 )
90.	Book Title The Origins of Feedback Control Author Mayr, Otto Date 1971 Grades 7-16 Keywords FEEDBACK HISTORY	Notes A detailed examination of physical methods for feedback throughout the history of civilization.
91.	Book Title A Computer Perspective: Background to the Computer Age Author Eames, Charles & Ray (Office of) Date 1973 Grades 7-16 Keywords COMPUTING DEVICES HISTORY	Notes The fascinating evolution of calculating machinery. The story of L. F. Richardson is amazing.
92.	Book Title The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine Author Petzold, Charles Date 2008 Grades 11-20 Keywords COMPUTABILITY HISTORY	Notes A journey through the work of the pioneer who invented computing and defined computability (with Church) before there were any computers; he may have also built the first one.
93.	Book Title A Beautiful Mind Author Nasar, Sylvia Date 1997 Grades 13-16 Keywords GAME THEORY HISTORY	Notes This book not only does a great job of describing Nash's career and contributions to game theory, it also supplies a lot of context about what else was going on in math. Trigger warning: he had some hateful views that would not fly in today's society.
94.	Movie Title A Beautiful Mind Date 2001 Grades 13-16 Keywords GAME THEORY< HISTORY/TD>	Notes The movie version is well made, lighter on math but also light on the hate.
95.	Book Title The Cybernetics Group Author Heims, Steve Joshua Date 1991 Grades 11-20 Keywords HISTORY OF CYBERNETICS	Notes A pedestrian but useful account of the meetings in the late 1940s where cybernetics was born.
96.	Book Title A Mind at Play: How Claude Shannon Invented the Information Age Author Soni & Goodman Date 2018 Grades 11-20 Keywords INFORMATION THEORY HISTORY	Notes An uplifting account of Shannon's career. [I have not read this book.]
97.	Book Title Information Theory and Coding Author Abramson, Norman Date 1963 Grades 13-20 Keywords INFORMATION THEORY	Notes A very serviceable text on Shannon's information theory.
98.	Book Title Theory of Games and Economic Behavior Author von Neumann, John and Morgenstern, Oskar Date 1944 Grades 7-16 Keywords SYMBOLIC MATH GAME THEORY	Notes The book that created the field of game theory.
99.	Book Title Design for a Brain Author Ashby, Ross Date 1952 Grades 8-29 Keywords CYBERNETICS, MACHINE LEARNING	Notes Ashby is always a delight. Here he is grappling with early concepts in machine learning.
100.	Book Title Cybernetics [Second Edition] Author Wiener, Norbert Date 1961 Grades 13-20 Keywords CYBERNETICS, FUNCTION PREDICTION	Notes Wiener's manifesto on the new science of cybernetics is important but mostly impenetrable. If you manage to figure it out please explain it to me.
101.	Book Title General System Theory Author von Bertalanffy, Ludwig Date 1968 Grades 11-20 Keywords SYSTEMS THEORY	Notes Working in Germany at the same time Weiner was working in the US, von Bertalanffy laid out a blueprint for systems theory and many of his ideas are still relevant today.
102.	Book Title Embodiments of Mind Author McCulloch, Warren Date 1970 Grades 7-16 Keywords NEURAL NETS	Notes A collection of McCulloch's papers on mostly neural nets. He was Bateson's mentor and the organizer of the Macy meetings where cybernetics was born.
103.	Book Title Fractal Geometry of Nature Author Mandelbrot, Benoit Date 1982 Grades 11-20 Keywords FRACTALS	Notes Mandelbrot's original manifesto on fractal dimensions, electrical noise, river flooding levels and the lengths of coastlines.

Final Thoughts

When I showed the 1990 Curriculum for Cybernetics and Systems Theory Version 1.0 to an educator I know, he said "This isn't a lesson plan." Well, version 2.0 isn't a lesson plan either, but it's closer. It's like a plan for a lesson plan. Unfortunately to complete the plan one must learn all of the subjects listed above, and read and become familiar with all the texts. But I wanted to capture my current thoughts on the subject. Expect more improvements.

Feedback requested as always.

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Last update: Thu Aug 18 19:27:57 PDT 2022