Math 105/Fall 2011

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Math 105-1, San Francisco Art Institute, Fall 2011

Systems, networks, and strategies
Thursdays, 7:30-10:30 PM, MacMillan Conference Room
This course surveys contemporary thinking about complex systems, coexistence and strategy, through a mathematical lens. We will explore system theories, cooperation, networks, and related ideas. We will use them as a framework to develop relevant math concepts, such as sets, algebra and statistics, and simultaneously explore their social context and think critically about ways to use and question them. Students will gain broadly applicable math skills and resources to develop them further, and a survey of culturally relevant discourses. The instructor will work with students to develop class projects relevant to their interests. Students will be evaluated on a mix of coursework and projects.

The initial request was for me to teach a course built around the idea of networks... I like the general idea - bouncing between current social ideas, political philosophy, etc. and math tools...

It's supposed to be a college-level math course, and I was concerned about whether just doing the systems, networks and strategy would be compatible with teaching math skills and giving students tools they can use. But I've been asked to shift the focus in that direction, and I think it will work.


        July                 August              September
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa
                1  2      1  2  3  4  5  6               1  2  3
 3  4  5  6  7  8  9   7  8  9 10 11 12 13   4  5  6  7  8  9 10
10 11 12 13 14 15 16  14 15 16 17 18 19 20  11 12 13 14 15 16 17
17 18 19 20 21 22 23  21 22 23 24 25 26 27  18 19 20 21 22 23 24
24 25 26 27 28 29 30  28 29 30 31           25 26 27 28 29 30
      October               November              December
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa
                   1         1  2  3  4  5               1  2  3
 2  3  4  5  6  7  8   6  7  8  9 10 11 12   4  5  6  7  8  9 10
 9 10 11 12 13 14 15  13 14 15 16 17 18 19  11 12 13 14 15 16 17
16 17 18 19 20 21 22  20 21 22 23 24 25 26  18 19 20 21 22 23 24
23 24 25 26 27 28 29  27 28 29 30           25 26 27 28 29 30 31
30 31                                       

Sept. 1, 8, 15, 22, 29
Oct. 6, 13, 20, 27
Nov. 3, 10, 17
Dec. 1, 8
= 14 weeks

Oct 20 = midterm grading
Nov 24 = holiday

Systems and models unit

Sept 1: Intro class

What is this course about, and who's in it. Cattle ranching game.

  • Lecture Outline: odt pdf
  • I added a brief Qi Gong exercise to help us be centered and calm, at the very beginning
  • When talking about math anxiety and stereotype threat I made some declarations of students' rights, inspired by this Math Anxiety Bill of Rights. See also Math Teacher's Ten Commandments.
    • I might have done well to talk specifically about gender and math (the 6th-grade thing), and to say it's also cool if people do feel good about the subject and like it!
  • the overview lecture was shorter and less well organized than I hoped.
  • used a brief survey (aka assessment) to find out what the students already have under their belts: odt pdf
    • Overall people seemed to know how to answer all but the last two, even if they got a couple wrong answers on the others. So they're a little better prepared than the baseline that I had been anticipating.
    • I hadn't planned to grade or return them, but the students asked me to. They also wanted to know on the spot whether they'd gotten the last two right or not.
    • the grid graphic that I used in the assessment
  • the tragedy of the commons activity is from Peter Taylor's Unruly Complexity: Ecology, Interpretation, Engagement. I made a lot of paper cows (svg, pdf) and paper money (svg) so we could physically buy and collect cows, though we could have done it just by writing down numbers of cows and dollars at each turn.
    • it seemed to me that the commons game helped us all become more engaged and interested.
    • it also involved more math than I expected. For instance, when the profit per cow dropped from $100 to $45, and some people had 17 or 29 cows, we all had to try to figure out how much total profit people were due. This was nice because we're all pretty much equally skilled at multiplying things, so it broke down the inequality between me and them.
    • I didn't anticipate that the sums of money would become so complicated: I only made $100 bills. One of the students realized before I did when the profit dropped to $45 that we were going to get odd dollar amounts, and asked me if I was going to round up to the nearest $100. I said yes, as if I had some kind of clue...
    • I wasn't completely clear on what Peter does and doesn't tell the students before or during the game. For instance, when the income started to drop, I told them it was because the common pasture was overcrowded. I also wasn't as clear as I would like to be (probably my own doing) whether to stop and discuss before the end of the activity, when to end the activity, whether to make suggestions or ask questions before the end, and what and how much to discuss afterward.
    • Student's choices during the game varied a lot:
      • one person saw that profit from cows was falling, so decided to sell them off to other players
      • several players wanted to sell cows back to me, but I wasn't buying
      • some people kept buying large numbers of cows, one "to see what would happen" and others for reasons I don't know
      • some people stopped buying
      • nobody tried to negotiate collective behavior with the other players
  • the tragedy of commons mini-lecture, after the activity, including Garret Hardin, Elinor Ostrom, allusions to Polanyi and the history of enclosure and dispossession of the land, current political movements about commons, and the inversion of the "tragedy", seemed to go well and students seemed interested. I think it helped make concrete what I had been saying about understanding models in their social/historical context and thinking critically about them.

Notes for next time:

  • My material went faster than I had planned. I need to have more material prepared, and I need to prepare my lectures more completely.
  • I need to bring dry-erase markers - the room didn't have any.
  • bring updated course roster and take roll again.
  • return the surveys with answers marked (I already marked them).

Sept 8: Simple models and linear systems

Systems I: Simple models and linear systems.

Intro to the conceptual toolkit. Variables, graphs, multiplication, division, fractions.

Learning outcomes:

  • be able to iterate a simple discrete-time map
  • be able to identify the function defining a discrete-time map
  • be able to plot the iterates of a simple map in phase space (i.e. on number line) and against time
  • be able to use terms:
    • variable, model, stock, flow, space, function, exponential growth

The sequence:

  • qi gong before we start
  • return the assessments and take roll. discuss the assessments.
    • go over quadratic formula, finding an average? if people want.
  • discuss the Lockhart reading, and whatever else.
    • amendments to math-anxiety bill of rights?
      • comments on girls + math/science: there's a drop-off in middle school for some reason
      • right to enjoy math regardless of your identity/intentions
    • talk about grading policy!
  • intro to lecture: what we're going to do
    • our first math models, what they look like and how we use them
  • two-in-and-one-out game
    • I think we should actually play it.
    • talk about the inflow vs outflow, net growth
    • plot on number line
    • plot x vs. t
      • independent, dependent variable "question, answer"
      • x against t.
    • x is state variable or dynamic variable, changes following a rule.
      • i.e. variables, dynamics;
      • numbers, axes, graphing, coordinates.
      • stock, flow.
      • what would happen with different parameters (inflow and outflow), i.e. write it as xx+a-b, vary a and b.
  • Project some early pages from Abraham and Shaw book
    • talk about states, trajectories. with examples. the geometric metaphor.
    • the state variables; the state space. the idea of a space.
    • trajectory
    • time series; relation between the two
    • more than two dimensions; strange spaces.
      • coordinates on Google maps? on paper maps? borrow a map from Robin?
  • look at the 2-in, 1-out model on number line (state space).
  • look at 2-in, 1-out model against time axis.
  • spend some time on notation.
  • exponential growth model.
    • x2x.
    • what it looks like on time axis.
    • what it looks like on number line.
    • effect of changing parameter.
    • xrx: exponential growth, exponential decay, oscillation
      • Fractions, negative numbers.
    • already the model is multivalent: is it bacteria, people, rumors? bank balance? inflation? a pyramid scheme?
  • talk about continuous-time models
  • If we get there, talk about density-dependent growth: xrx(1-1Kx)
    • explore
  • Lecture about history, context of these ideas?
    • multiple models for the same thing, a single model for multiple things
    • the same model in biology, physics, economics, engineering...
    • generalization of dynamics ideas - exponential growth; stocks and flows; oscillation
    • general system theories
  • if time permits, watch some of part 2 of Adam Curtis's All Watched Over by Machines of Loving Grace - that's the one about equilibrium, the balance of nature, and trust in systems and self-organization.

unresolved thoughts

  • do some system dynamics in Excel?
  • Could play with population dynamics for a good while.

Things to preteach for Abraham

  • we'll go over the pages in the lecture, above.

Things to preteach for Meadows:

  • leverage points (The silver bullet, the trimtab, the miracle cure, the secret passage, the magic password, the single hero or villain who turns the tide of history)
  • Jay Forrester; limits to growth (Forrester in Curtis video?)
  • parameters
    • size of bathtub, max rate in, rate out
  • stocks
    • buffer = big stock
  • flows (inflows, outflows)
    • like in 2-in, 1-out game
  • delays
    • shower on 4th floor
  • feedback
    • negative feedback: controlling faucet + drain in bathtub; density dependence
    • positive feedback: population explosion
      • tragedy of commons = missing negative feedback?
  • modeling a system in a computer
  • changing the structure of the system
  • self-organization = system changing its own structure?
  • paradigms

reading to take home:


  • write values of x(t) for some cases of the rx and x+a-b system, for t=010 or so
  • plot them on number line and against time
  • predict long-term behavior
  • do a 2-variable system.
    • plot on 2-D state space, and on 2 time series.
    • (extra credit: make a 3-d plot somehow!)
  • do a couple rx(1-x) problems.
    • a fixed point, a period-2, and a chaotic one
  • here's the homework: odt, pdf

To do before class:

  • arrange for projection
  • get dryerase markers
  • photocopy the assessments
  • create recordkeeping system
  • record and aggregate the assessment results
  • reread the Lockhart essay
  • scan in the Abraham pages
  • write the homework
  • review the "ten commandments"
  • print Abraham, Meadows, homework, lecture notes
  • get course roster
  • bring course roster
  • bring assessments
  • write class outline on whiteboard
  • for projection:
    • open the files to project
    • turn off email alerts (or just quit thunderbird)
    • turn off skype
  • cellphone off

Post-lecture notes:

  • The students did not grasp the material fully - I think they all understand how to keep adding one to a number or keep doubling it, so the trouble is with the language and notation.
    • In particular, I didn't give enough attention to the idea of a function - I took for granted that the function notation would be understood.
    • Not only that, but I was using it in at least two different ways:
    • How could I expect the students to absorb both of these things at the same time and use them both in a single expression without being confused and frustrated?
  • I think I want to redo this part of the lecture without any functions
    • just xnext=2x, and xnext=x+i-o, etc.
    • do all the rest in words. If the first value of x is 3, what is the next value? what's the third value?
    • At the first step (time 1) and subsequent steps, plot the value of x against the number of steps taken so far? tricky.
  • Give them a complete orientation to start with. What are we learning to do and what can you use it for?
    • We are learning to iterate a map as an example of a mathematical model.
    • Once we learn these simple maps we can use what we've learned to talk about how we would do more complicated examples.
    • We can use the 2-in, 1-out game to examine how stocks and flows work, and apply our knowledge to many different situations
    • We can use the population explosion model to talk about a range of explosive events, from cultural change to bombs and potential nanotech disasters.
    • The family of four exponential models (in the homework) demonstrates the four major kinds of behavior near an equilibrium.
  • But what can you use them for?

Sept. 15: Feedbacks and circuits

Systems II: Feedbacks and circuits.

Deeper into ideas about systems and what they do. Solving for variables, plotting functions. More models, including maybe a little physics.

Learning outcomes:

  • be able to iterate simple discrete-time maps
    • write down the first few values
    • plot them on number line
    • plot them against t
    • predict the long-term behavior informally
  • be able to use terms:
    • variable, model, stock, flow, space, exponential growth
    • positive and negative feedback, system

Class outline:

  • start w qi gong
  • open questions and discussion
  • discuss the Meadows reading a little - we'll talk more in the second half.
  • project ideas
    • the wiki URL
  • Pe Lang coming up; we'll do systems + art next time
  • revisit the math from last week - 90 minutes at most.
    • why are we looking at these models?
      • I'm doing the class in two parallel threads - one in English about ideas + history, one in math language about how models work
      • I don't just want to talk about the history of ideas about systems, I want to share the experience of working with them from the inside
      • we can look at the meanings and consequences of these models together when we have the models themselves on the table between us
      • stocks and flows suggest ability to control a system
      • exponential growth is unrealistically unbounded
      • Malthus
      • exponential decay is the purest example of an equilibrium (a keystone of modernist mythology, as we will see in the Curtis video)
    • hand out revised homework, look at it together
    • new notation: "xx+1" and "x2x"
      • is this notation understandable? can we use it to
        • find the first few values
        • plot them on the number line
        • plot them against t
        • predict what will happen in the long term?
    • if so, do the first HW problem together
    • then do exponential decay together
    • prep for the other examples in the homework.
  • --break-- if we haven't already
    • run and revise/reprint the homework if necessary
  • talk about systems, feedbacks, cybernetics, preteach the next reading (45 minutes)
    • history of cybernetics and quantitative systems modeling
      • it doesnt' really start with Wiener, goes back to the Chinese, the Greeks and the steam engine. Also Ampere, Cybernetique, science of governance
      • Condorcet on voting and progress?
      • WWII and emergence of idea of feedback along with operations research
        • negative feedback: guided missile example, family example ?
          • Cybernetics = steersman? Governance.
        • a feedback comes with a causal circuit, which gives us a system.
        • the need to study the system, in distinction to the components
          • examples: maybe Meadows' shower example
          • therapy example in reading
          • governance... managing interest rates... people organize or riot when things get bad... Bateson + Haley's debate about power, political consent
      • negative vs. positive feedback
        • video: Jimi Hendrix and/or Sonic Youth
      • People study systems, including complicated ones
        • Idea of "general systems theory"
        • graphical examples of system diagrams and models
      • things cybernetics people did
        • Cybernetics and Norbert Wiener's life
        • Is it military in nature? It seems to go to other places - study of governance, freedom, love.
        • Ashby's machines + learning (kitten learning from mouse)
        • Pask's color machine, growing computers
        • McCullough's neural networks
        • Bateson's anthropology of difference and sameness; plateaus; wartime work
        • Stafford Beer, Project Cybersyn in Chile, corporate downsizing
        • Gaia, ecosystems
      • Cybernetics in the 60s
        • became popular as way of rethinking the world, new paradigm, holistic... whole earth... connectedness...
        • Gregory Bateson, Stewart Brand and Jerry Brown
        • holistic vs linear thinking.
        • the structure of the system vs. the nature of its parts.
        • idea of a system seems to contradict idea of leadership.
      • Cybernetics and computers/machines/corporations/military/domination
        • Deleuze, society of control, globalization
  • Give out the readings
    • dependent co-arising
    • skip abstract, last 2 sections of therapy paper
  • show the video (1 hour):

Hand out

  • write lecture notes to hand out?
  • revised homework (odt, pdf)
  • readings:
  • readings I considered but am not using:
    • I'd like to use Deleuze's Society of Control but it has a lot of theoretical prerequisites
    • Or Michael Hardt's Global Society of Control
    • or intro-to-systems-and-feedbacks chapter from The Fifth Discipline?
    • can't I find a good intro to feedback and cybernetics from someone I like?
    • "The Systems View of Life" from Capra, The Turning Point - is a useful roundup but a bit much - maybe just some of it. It isn't self-contained - refers to a lot of science ideas.

To do

  • rewrite the homework
  • print the homework
  • print the readings
  • get the lecture notes all ready
    • including project ideas
  • computer ready to project (email and skype off, projector on, video(s) loaded)
  • review of key concepts to write on the board
  • review the Meadows reading
  • preteaching for this week's reading
    • dependent co-arising
  • find a good guitar feedback video?
  • Who is Pe Lang? Have something to say to preteach these "Simple Mechanisms - Strange Behavior" events.
  • After: mark, photocopy and return the class roster(s)

Postmortem notes:

  • I stopped the video at 24 minutes because it was time to leave
  • I didn't say all I wanted to about the cybernetics people, Bateson and Walter for instance. Next time if we screen the rest of the Curtis video maybe I'll say something about Brand and Bateson, and throw in the rest as well.
  • After I did the re-lecture on the homework problems, I wasn't sure whether I had everyone with me. I had to just leave it and wait to see when I collect the homeworks. I'd rather stick to it and do what it takes to keep us together, but when students don't want to engage that way maybe I have to respect their wishes? Maybe there's a way to invite them.

Complex systems pre-unit

Sept. 22: Rules and outcomes; equilibria

I am changing the sequence a bit to connect with the opening of this "Simple Mechanisms - Strange Behavior" show. So I'm going to do some of the complex systems material now, and some of the simpler systems stuff next time. That fits better with the homework sequence anyway.

Complex systems I: rules and emergence

Simple mechanisms - strange behavior

Systems III: equilibria and stability

More ways to think about change and times without change. Plotting more advanced functions, thinking about more complex systems and models.


  • Collect homework
  • Hand out ideas for projects
  • Discuss the art show
    • Dancing robots and swarm intelligence
      • ants, bees, termites; emergence; stigmergy
      • swarms of people (or robots); centralized vs distributed coordination; nomads vs the war machine; WTO protest + subsequent; al-qaeda; USAF swarming tactics
      • swarming intelligence for who? who funds?
    • Quantum neon light sculpture
      • spin systems
  • Rules and systems in the art world
    • Cage, Rauschenberg, Xenakis
    • Sol LeWitt
    • Allan Kaprow
    • Herbert Brun
      • contradictions, perturbations, composing, anticommunication, false statements
    • Eno
      • One of Eno's favorite quotes, from the managerial-cybernetics theorist Stafford Beer, would become a fundamental guiding principle for his work: Instead of trying to specify it in full detail," Beer wrote in his book The Brain of the Firm, "you specify it only somewhat. You then ride on the dynamics of the system in the direction you want to go." Eno also derived inspiration from Stafford Beer's related definition of a “heuristic.” “To use Beer's example: If you wish to tell someone how to reach the top of a mountain that is shrouded in mist, the heuristic ‘keep going up’ will get him there,” Eno wrote. Eno connected Beer's concept of a “heuristic” to music.
    • 12-tone composers? Reich, Riley, Oliveros, ...
    • Kesey's Acid Tests, Brand's Trips Festival, "be-in"
      • the Well and creating environments for online communities
  • Rules and games
  • Followup on feedbacks + systems
    • perturbation
    • holism vs reductionism; the whole system
    • Goal-oriented behavior
    • self-organization + autopoiesis; the coming readings
  • the mathematics of equilibrium
    • back to the math: maybe a simple density-dependence population model?
    • how simple? xrx(100-x)? Yes, because we can deal with it graphically.
    • cobweb diagram, to find trajectories and equilibria
    • this is a different kind of plot, spend some time with it
    • do small r, system goes to equilibria
    • if going well, do larger r with a 2-cycle. otherwise leave this for next time.
      • look closer at the unstable equilibrium.
    • equilibria can be stable or unstable.
  • show the rest of the video
    • if there's time!
  • if there's extra time (ha! ha!) talk with people about what projects they'd like to do


    • Something on stable and unstable equilibria
    • Should I write lecture notes for the students to take home??
    • Ant colonies and brains, from Godel Escher Bach?
    • none of the above.
      • Barry Commoner's presentation on whole systems and ecological catastrophe, from Our Own Metaphor
      • Chapter on self-organization from Capra's The Web of Life.

Homework (odt, pdf)

Save for next time, probably:

  • the rest of the Curtis video
    • criticism of ideology of equilibrium, faith in emergent order
  • More on cyberneticians?
    • Brand, Bateson and Jerry Brown

Sept. 29: Chaos and overview of complex systems

Complex systems I: Complex systems and emergence.

Systems made of a lot of small parts, and the strange things that they can do, some of them very familiar. A look at cellular automata and some other frameworks.

Systems III: Equilibria and Stability

More on equilibria, non-equilibrium attractors, a little chaos

→ Proposals for first project due.

  • Once again, maybe show the second half of the video...
  • Continue lecture on equilibria, stability and attractors, leading on to an intro to chaos
    • I just got to unstable equilibria and cycles last time, using the cobweb diagrams with xrx(1-1Nx).
    • Erratum from last time: If it's 1Kx in the model definition, then K isn't the carrying capacity (I was thinking of the continuous-time model)
    • introduce attractor.
      • point attractors, periodic attractors (limit cycles).
      • basin of attraction.
      • initial conditions.
    • Review the basic facts and definitions about chaos
  • Intro to themes of complex systems
    • emergence of properties of the whole from the interaction of the parts
      • not chaos but order
      • brain, economy
    • self-organization (prigogine)
    • systems where the simple systems approach doesn't work - too many variables, or no equilibrium (economic bubbles) or indeterminate outcome (evolution)
    • show some cool videos
    • creation of Santa Fe Institute and its interdisciplinary approach
      • More is Different
    • economics
      • Brian Arthur, increasing returns
        • alternative to supply/demand equilibrium - economic system in flux, chaotic, changing
      • modeling stock markets, bubbles
    • biology
      • Kauffman's Boolean networks
        • tangle of light bulbs + wires genetic network
        • what happens? simple attractor! there are a small number of them!
        • Cell types! Origins of Order! The missing half of evolution! (my punctuation here is somewhat tongue-in-cheek)
      • Artificial Life
        • Tom Ray version
        • Chris Langton version / von Neumann
      • Cellular Automaton
        • 1-d video
        • CA and the "edge of chaos"
        • game of life
          • if alive, 2 or 3 live neighbors to stay alive
          • if not alive, 3 live neighbors to come to life
          • video - some configurations are open-ended, some aren't
        • back to Chris Langton
        • aside: Grey Walter version
          • 'At the end of an essay on cybernetics that Grey wrote in Colin Ward's Anarchy #25, 1963, (one shilling and sixpence), and which lies here open in front of me, he concluded: "we find no boss in the brain, no oligarchic ganglion, or glandular Big Brother...If we must identify biological and political systems our own brains would seem to illustrate the capacity and limitations of an anarcho-syndicalist community."'
        • contemporary version (Venter, synthetic biology)
      • genetic algorithm
        • Darwin = patron saint of SFI?
        • evolving CA
        • classifier system
      • Fontana's autocatalytic networks
        • origin of life; economics, ecosystems, industry, computing, culture/science
        • Rosetta Stone for Connectionism
          • neural nets, classifier systems, immune networks, autocatalytic reaction networks (and others)
    • ants + swarm intelligence
      • Ants vs. neural networks
    • sandpile
      • has been used to describe economics, puctuated equilibrium, cancer, political/social change, scientific paradigm shifts, climate change
    • Immune system information processing
      • designing an immune system for computers
    • mention Scott Page's nice result
    • SFI researchers published an important result in HIV research at one point - what was it?
    • Agent-based models in ecology and social sciences
    • mercury beating heart
    • Iain Couzin flocks
    • Mandelbrot


  • Chaos
  • chapter 1 and 3 of Waldrop's Complexity (Arthur and Kauffman)
    • maybe just the Kauffman chapter and
    • part of the ant colonies and brains dialogue from Gödel, Escher, Bach
  • bring extra copy of the feedback readings for student who lost them

To do

  • new homework assignment? solving for equilibrium with algebra? or making bifurcation diagram qualitatively, using cobwebs somehow?
  • comments on 9/29 homework
  • photocopy the 9/29 hw before returning
  • reading
  • survey: (odt, pdf)
  • flesh out lecture, sequence of videos


  • I only got partway through the complex systems, and I think I'll pick it up again next week even if it means lagging behind the syllabus.
  • also, in the chaos lecture I didn't get to the period doubling bifurcation diagram, and it wold be nice to do that next week.
  • Heard students' project proposals and am inspired!

Interests and strategy unit

Oct. 6: Cooperation and temptation

Strategy I: Cooperation and temptation.

Is it hard to be nice? Critical thinking about science and cooperation. Game theory, some standard economics. Several relevant models. More game playing.

But first, more of the complex systems lecture

  • left off somewhere around here
    • CA
      • game of life
        • if alive, 2 or 3 live neighbors to stay alive
        • if not alive, 3 live neighbors to come to life
        • video - some configurations are open-ended, some aren't
      • back to Chris Langton
        • CA and the "edge of chaos"
    • Artificial life
      • Langton CA video?
      • Tom Ray?
      • aside: Grey Walter version
        • 'At the end of an essay on cybernetics that Grey wrote in Colin Ward's Anarchy #25, 1963, (one shilling and sixpence), and which lies here open in front of me, he concluded: "we find no boss in the brain, no oligarchic ganglion, or glandular Big Brother...If we must identify biological and political systems our own brains would seem to illustrate the capacity and limitations of an anarcho-syndicalist community."'
      • contemporary version (Venter, synthetic biology)
      • genetic algorithm
        • Darwin = patron saint of SFI?
        • evolving CA
        • classifier system
      • Fontana's autocatalytic networks
        • origin of life; economics, ecosystems, industry, computing, culture/science
        • Rosetta Stone for Connectionism
          • neural nets, classifier systems, immune networks, autocatalytic reaction networks (and others)
        • all at edge of chaos?
        • Immune system information processing
          • designing an immune system for computers
    • ants + swarm intelligence
      • Ants vs. neural networks
    • sandpile
      • has been used to describe economics, puctuated equilibrium, cancer, political/social change, scientific paradigm shifts, climate change
      • self-organized criticality - solid/liquid phase transition; self-organization to edge of chaos
    • mention Scott Page's nice result
    • SFI researchers published an important result in HIV research at one point - what was it?
    • Agent-based models in ecology and social sciences

Cooperation and temptation lecture

  • Return to the tragedy of the commons from the first day
    • the scenario
    • the history - Hardin
      • policy prescriptions: privatize, public management
      • Ostrom, Berkes and others: actually many traditional communities do quite well at managing resources held in common
    • the older history - traditional common-resource management, enclosure movement, resistance, dispossession, wage labor, contemporary enclosure struggles.
      • Boston Commons; “They hang the man and flog the woman, That steal the goose from off the common, But let the greater villain loose, That steals the common from the goose”
      • "commoning" and a third form of property
  • The Prisoner's Dilemma
    • (2031)
    • Cooperate, defect.
    • The standard story - police, suspects.
    • Bottom row dominates.
      • Temptation to defect.
    • Play classroom game 1.
      • Give each person a red card and a black card. Black = "push" $2 to your partner, take nothing for yourself. Red = "pull" $1 to yourself, give nothing to partner.
      • Lay down one card, then I assign pairs at random. (six-sided die?)
      • Play a few times.
      • Payoff is in fake $100 bills.
    • Play classroom game 2. Same, but know in advance your neighbor is your partner.
      • Play a few times.
    • Play game 1 again. Just one time. See how people play now.
  • Return to the matrix, discuss Nash equilibrium
  • N-person social dilemma.
    • Tragedy of commons
      • non-excludable: everybody can partake, regardless of whether they contribute
      • subtractible: when people use it it becomes less available for others.
    • Public goods
      • non-excludable but non-rival (the opposite of subtractible): my use of it doesn't diminish your use of it.
      • Public radio, for instance
      • Free riders
    • Collective action problem
      • contribution to public radio, participation in politics (voting, protesting, paying taxes, ...)
  • Play social dilemma game: black = push $1 to every other player, red = pull $2 to yourself
  • History of prisoner's dilemma studies.
    • repeated play, tournaments, computer tournaments, Tit-for-tat solution (reciprocal altruism). Evolutionary computer tournament.
    • Other solutions: communication, tags, spatial proximity, relatedness, application of heuristics developed in other settings, group selection, reputation, a norm of conformity, punishment, incentives (see for list with citations).
  • mention my escape from prisoner's dilemma and related results, Turner and Chao for example. Save sequential selection for the Darwin unit, when we will talk about Gaia.
    • Existence of alternative games - chicken (2130) (snowdrift; hawk-dove), assurance (3021), byproduct cooperation (3120).
    • Play byproduct cooperation game with your neighbor, for cookies. Use the cards.
  • Ways to think critically about claims about cooperation and temptation and altruism. (Numbered items are from Peter Taylor's paper and his book.)
    • Question the structure of the game. Some famous "prisoner's dilemma" scenarios are actually snowdrift, chicken, or even byproduct cooperation games, if they're two-person games at all, and the same caveats and more go for N-person games and "tragedies".
    • Question the assumption of "rational self interest". Sometimes people have other-regarding preferences.
    • Question the limitation to two choices. There are usually others. Positive social change often is often created by discovering or inventing new options when the ones that are given aren't sufficient.
    • 1. Interpret systemness as problematic. What's been declared extraneous to the system?
      • possibility of changing the system's dynamics. For example, changing the game to a different one.
      • connections not acknowledged, for instance social relationships between "game players"
      • boundaries of the system are seen as permeable
      • Inequality among individuals within the system colors their options, including response to developments "outside" the system
    • 2. Interpret the rhetorical effects of models
      • "simpling": "Like sampling, 'simpling' is a technique for reducing the complexity of reality to manageable size. Unlike sampling, 'simpling' does not keep in view the relation between its own scope and the scope of the reality with which it deals ...It then secures a sense of progress by progressively readmitting what it has first denied. 'Simpling' ... is unfortunately easily confused with genuine simplification by valid generalization." (Hymes 1974, See Taylor for citation)
      • reinforcing foundational assumptions, for instance self-interested behavior, liberal idealization of "mankind" all equal
      • privileging certain interests. For instance use of the T.O.C. model strengthens the political position of players with disproportionate power, since it makes the effects of inequality invisible. Who benefits?


To do:

  • Videos for complex systems lecture
  • Write homework
  • Watch Adam Curtis part 3, decide whether to show
  • Work out why the Holt paper has payoffs of $2 and $3 for the card game - I have changed it to $1 and $2, does it make a difference?
  • Bring deck of cards.
  • Bring $30 in $1 bills.
  • Bring cookies.


  • I decided to leave the complex systems lecture for another day, when I have collected more video to show or something. Today I just did the cooperation lecture (partly because I wanted to do it all on one day, not continue it across two classmeetings) and showed part of the 3rd installment of the Adam Curtis documentary afterward.
  • I did a crowdfunding experiment to raise $30 for the cash game from donors on the internet, and ultimately raised $36 (I'll give the surplus back).
  • Generally people were inclined toward cooperating ("pushing"). I walked them through the logic of the game multiple times, and they were not swayed:
    • Me: it's true that if you both cooperate you get more than if you both defect; but if you are both going to cooperate and then you cheat at the last minute you get even more!
    • Student: Yes, but if we do that we'll only get $1.
  • There was a little cheating, but for the most part they stuck to cooperating and got the good rewards.
  • I don't think the two pairwise games were as different as I hoped - playing against an unspecified opponent doesn't make much difference when the choices are going to be known publicly and your reputation will be affected. I'm curious whether it would make more difference if it was fully anonymized in the sense that people put their choice in an envelope and get their payoff in an envelope so that no one ever finds out whether they defected or not.
  • They weren't very interested in communicating with each other when the pairings were known, and before the social dilemma game. They seemed to just want to try to figure what the others would do, and make their own choices.
    • This is also a case of a more general dynamic in the classroom - they want to know what they're "supposed" to do. Before the cash game I asked them, do you want to talk with each other? and one student asked me, are we supposed to talk to each other? I said I don't have an opinion whether you should talk to each other, I'm interested in whether you choose to. In general, my point of view is that they're basically paying me to come and teach them, and they're allowed to do whatever they want, and their point of view seems to be that they're trying to find out what they're supposed to do. I think I've done pretty well at giving them structure around how to do the projects without bossing or constraining them - I want to get better at giving them guidance while creating space for them to figure out what they want in the rest of the class.
  • One student (at the break) pointed out a very concise critical response to the prisoner's dilemma scenario that I had left out: a good rule of thumb is "never talk to the police". They are allowed to lie to gain a confession, so there's no reason to think that "defecting" will actually get you any payoff other than a beating and a long sentence. Also, anything we say can be used against us and against our friends and loved ones, potentially in surprising ways that we wouldn't anticipate. This is why lawyers frequently advise us to say nothing but "I am going to remain silent. I would like to see a lawyer." if detained. This goes right to several of my "ways to think critically", particularly "question the structure of the game".
  • There weren't as many people there as usual - 3 students plus me, so I debated whether to raise the payoffs for the $$ game - I decided not to because I was worried I'd do the algebra wrong and end up overshooting the $30...
  • The first time we played for money, at least one student didn't understand I was going to let them keep the money.
  • Because there's a squared term, playing with 3 people pays way less than with 5 or 6. After we played it and discussed it some more, I decided to play a second time. They played the real-money social dilemma game flawlessly both times, and only got $6 apiece total. (The left-over $12 pays almost exactly for the cookies.)
  • At least one student thought that it would need to be higher stakes before they would be tempted to defect. I think this makes sense in terms of reputation.
  • When we played the byproduct cooperation game at the end, I got flustered about the calculations - I played along with them (so 4 players) and we all cooperated of course, so the payout was 8 cookies each - are there really enough for everyone to take 8 cookies? I think actually there was, but I became afraid I'd calculated wrong and there wasn't. I don't think anyone actually wanted to take 8 cookies anyway - people took 2 or 3, and I hope everyone was okay with that.
    • They were vegan cookies, but not gluten free. Fortunately, no one was gluten intolerant. I got to take some home, which made me happy.
  • The 3rd installment of the documentary is kind of scattered and doesn't seem as useful as the 2nd installment. I showed the first 30 or 40 minutes, so I'll show the rest, but whatever. It provides a little human interest about Hamilton and Price, and includes Dawkins, but doesn't introduce their ideas in much depth and doesn't criticize or place them in cultural context nearly as much as I would like. Also I wished he would have included the Robert Trivers-Huey Newton connection - I bet he would have if it'd been an American documentary. I'll have to see if I can fit that into my lecture.

Other Notes

Oct. 13: Natural selection

Strategy II: Natural selection.

Genes, evolution, and their politics. Exponential growth, some statistics. More models.

  • Darwin's history, the basic ideas
    • Natural selection, descent with modification
    • How it works
      1. Variation: some individuals in a population are different from others.
      2. Heredity: offspring resemble their parents more often than they resemble unrelated inviduals.
      3. Natural selection: different variants leave different numbers of offspring
    • This looks like a good activity (got it from here).
    • models?
  • Evolution in independent environment optimizes something.
    • sketch of adaptive dynamics model framework.
  • When environment is not fixed all kinds of things can happen
    • general dynamical system
    • We might expect the traits we observe to be adaptations, i.e. the result of optimizing; but they could be an exaptation as Gould argued, and could also be the result of an evolution process that does not optimize -- evolution can even pessimize, even in a one-species system, when the population affects the environment: you can have a tragedy of the commons outcome.
    • Mention the Gaia controversy, but we'll discuss it later
  • Mendel, genes, the modern synthesis
    • flowers, crosses, recessive/dominant genes?
    • phenotype and genotype
      • the pathway from genes via RNA transcription, folding to proteins, cellular functions, cell types, tissues, bodies, behaviors, survival and reproduction
      • the central dogma; Darwinian vs. Larmarckian ideas
  • Genes are selected for/against, tend to fixation/extinction
    • Mutation + selection adaptation by natural selection
    • The network of genes' effects; genomics (epigenetics?)
    • Genes "for" traits
  • evolution is a kind of adaptation process
    • evolution of things other than organisms
      • culture, institutions, technologies. universes?
    • other adaptation processes including learning
  • gradual vs. punctuated
    • political resonance of Eldredge/Gould paper
  • does evolution make progress?
    • when we say it does we are reifying the politics of Eurocentric domination, faith in science and technology, etc.
    • hence Gould's argument to the contrary. Humans are not "higher" than bacteria, just newer.
    • does complexity increase? It's not clear. Meanwhile, it's not like the bacteria are going away.
    • but Kauffman's adjacent possible is a nice frame.
  • Levels of selection
    • group selection
      • the altruism question
    • gene selection
      • the selfish gene
        • example
      • kin selection and altruism
  • fitness and self-interest. Payoffs. Evolutionary game theory.
    • conflicts between organisms. Predators and prey. The Red Queen hypothesis; evolutionary arms races.
    • general mashing up of political, economic ideas into evolutionary theory. Capitalist biology.
      • "Putting an optimization program into practice requires a general theory of optimality, which evolutionists have taken directly from the economics of capitalism. It is assumed that organisms are struggling for resources that are in short supply, a postulate introduced by Darwin after he read Malhus's Essay on the Principle of Population. The organism must invest time and energy to acquire these resources, and it reinvests the return from this investment partly in acquiring fresh supplies of resource and partly in reproducing. ... The optimizing theory of allocation assumes that time allocation will be close to optimal for maximizing total investment in reproduction, or growth of the firm. In such theories the criterion of optimality is efficiency, whether of time or invested energy, yet the moralistic and ideological overtones of "efficiency," "waste," "maximum return on investment," and "best use of time" seem never to have come to the consciousness of evolutionists, who adhere to these social norms unquestioningly." The Dialectical Biologist, pp. 25-26
  • Evolution vs. religion
    • Monkey trials. Current fights about textbooks and curriculum.
    • Dawkins, PZ Meyer, etc.
    • Orthodox priesthood of science vs. centralized institutions of religion - less hierarchical spiritual traditions are made invisible
    • Some people, even Christians, disdain scientific authority including evolution theory less because of adherence to dogma than because of rejection of technoscientific modernity, in full view of its disastrous consequences and the sound reasons for mistrusting scientistic authority - the Tuskegee experiments, the atomic bomb, X-rays, thalidomide, carcinogenic food, internal combustion and carbon emissions, etc.
    • Rich, powerful white men in the US and Europe heaping scorn on Christians and Muslims alike is politically tone-deaf at best
  • Evolutionary theory and structural inequality
    • Darwin was inspired by Malthus's scarcity scenario, which is a flimsy rationale for class oppression and deeply interwoven with racist ideologies of the 19th century
    • Darwinism adopted by racist, elitist Social Darwinists; Kropotkin's book is major response
    • Eugenics; Nazi history, but also racist science in US, Europe
    • Modern-day eugenics; contestations over Human Genome Project; Larry Summers at Harvard; "Gay Gene"; prospect of human genetic enhancement, emergence of elite subspecies; selective abortion of girls, disabled, lgbtq children
  • Reductionistic and holistic biology
    • Genes are the atoms of the 21st century, the big funders are looking for the new Manhattan project -- the greatest "triumph" of reductionist science
    • you can't actually do much with genes without understanding them in context - hence systems biology - genomics, proteomics, etc. - which is difficult and tends to confound people's expectations of clear understanding and control.
    • Transgenic experiments, evolutionary escape, ecological impacts - failure to understand what will become of these organisms in context.


  • Stephen Jay Gould, Kropotkin was no Crackpot
  • Ruth Hubbard interview about "the gay gene" and politics of genetics generally.
  • maybe "Evolution as Theory and Ideology" from The Dialectical Biologist. This is a great survey of evolutionary ideas and critical responses to them, but it will be difficult reading, so maybe I'll make it optional.


  • critiques of Dawkins. critiques of gene ideology. Levins and Lewontin.
  • Evolution and economics
  • ecology, ecophilosophy. "balance of nature" vs flux.
  • game theory and rational man. Nash's claims. von Neumann and Wiener.
  • science and democracy. consensus vs. autonomy vs. central authority vs. privatization.
  • Wendell Berry, home economics... randomness...
  • I could go on and on
  • Dawkins' biomorphs; artificial life. Grey Walter.

Notes taken afterward.

  • I'm glad I paused at the beginning to open a space for what people know and think about evolution, because it turns out I have a Christian student who doesn't believe in it! I told her that a scientist in a science class would be likely to present a case to convince you that evolution is true, but I'm a mathematician, mostly interested in natural selection as a pattern of change in various systems, and I don't really care who believes what. Also, I think a lot of scientists who have contempt for religion are ignorant, insensitive and culturally or politically inappropriate.
  • Overall I wasn't at my best and I was sadly prescient when I wrote "I could go on and on"... The end of the class found me sort of staring glassy-eyed into space and fulminating about the warring institutions of science and religion when one of the students gently informed me that the class period ended 5 minutes ago!
  • Also I only got to partway through "Evolution and religion", so the rest will probably show up in the Oct 27 lecture.

Oct. 20: First project presentations

First project presentations.

I'm expecting:

  • An experimental film made by using random numbers to determine the order of lines, who speaks which lines, where and how they are delivered.
  • Something on art history as a succession of movements seen through the lens of positive and negative feedback.
  • A report on Norbert Wiener.
  • A presentation on gear ratios on bicycles.
  • A personal look at the presenter's own work process over a period of weeks as a system, with attention to the different inputs and influences.

I'm thinking of bringing:

Random numbers

  • flipping a coin
    • what does it mean that each side is equally probable?
    • probability, odds
  • probability theory's relation to gambling
    • What are good odds for a coin flip? a die roll?
      • value of inside information
    • mention the law of large numbers
    • the average
  • probability distribution
  • Something to do with the movie? Like how many different movies were possible?
    • that's combinatorics
  • How random numbers can be involved in a system's dynamics
    • maybe the outcome is made directly from random numbers
    • or maybe random numbers are an input into the dynamics
      • evolution for instance: mutation (random) plus selection (may be partly random but the most important part isn't)
        • history of art movements? influences on individual's process?
      • example of a simple dynamic system with random component
        • stationary distribution instead of deterministic equilibrium/attractor
  • Wiener process

possible handout

not going to show but I like it:

This is interesting as well, making a case that Wiener is a sort of father of the copyleft and piracy movements:


  • Yep, they were pretty good.
  • Also, I learned this week that the McMillan room, where we meet, was where Jay Defeo's masterpiece, The Rose, was stored for years after she was evicted from the apartment where she made it.

Oct. 27: Coexistence and coordination

Strategy III: Coexistence and coordination.

Thinking about economics and evolutionary biology together. Maybe some cybernetics.

  • Give people a report on their midterms grades situation
  • Review of where we've been so far
  • Talk about projects from here forward
    • pass out project ideas (odt, pdf)
  • pass out homework (odt, pdf)

Material left over from Oct. 13:

  • Evolution vs. religion
    • Monkey trials. Current fights about textbooks and curriculum.
    • Dawkins, PZ Meyer, etc.
    • Orthodox priesthood of science vs. centralized institutions of religion - less hierarchical spiritual traditions are made invisible
    • Some people, even Christians, disdain scientific authority including evolution theory less because of adherence to dogma than because of rejection of technoscientific modernity, in full view of its disastrous consequences and the sound reasons for mistrusting scientistic authority - the Tuskegee experiments, the atomic bomb, X-rays, thalidomide, carcinogenic food, internal combustion and carbon emissions, etc.
    • Rich, powerful white men in the US and Europe heaping scorn on Christians and Muslims alike is politically tone-deaf at best
  • Evolutionary theory and structural inequality
    • Darwin was inspired by Malthus's scarcity scenario, which is a flimsy rationale for class oppression and deeply interwoven with racist ideologies of the 19th century
    • Darwinism adopted by racist, elitist Social Darwinists; Kropotkin's book is major response
    • Eugenics; Nazi history, but also racist science in US, Europe
    • Modern-day eugenics; contestations over Human Genome Project; Larry Summers at Harvard; "Gay Gene"; prospect of human genetic enhancement, emergence of elite subspecies; selective abortion of girls, disabled, lgbtq children
  • Reductionistic and holistic biology
    • Genes are the atoms of the 21st century, the big funders are looking for the new Manhattan project -- the greatest "triumph" of reductionist science
    • you can't actually do much with genes without understanding them in context - hence systems biology - genomics, proteomics, etc. - which is difficult and tends to confound people's expectations of clear understanding and control.
    • Transgenic experiments, evolutionary escape, ecological impacts - failure to understand what will become of these organisms in context.

Other material

  • The blurring between biology and society in metaphors of interest, politics, economics
    • Frontier of utility
    • Optimization on boundary of fitness set [1] for example
      • these are essentially the same model
    • "Diversifying your portfolio" to manage risk, whether you are a pension fund or a milkweed
      • cast seeds far and wide so if there's a drought or landslide, some seeds will be elsewhere
      • put some in the "seed bank", i.e. have them lie dormant for some years so if there are bad years they will be around afterward.
    • "Biological markets", "Bionomics"
    • Is there Capitalism, Marxism in biology?
    • We tend to project features of our current society into nature - biological markets, for instance - but if we were less resistant to considering alternative social possibilities we could also consider things we see in nature as things we could do socially... byproduct mutualism for instance
  • Gaia theory
    • has come up several times in the readings by now.
    • Cybernetics proposition: the biosphere is a coherent system that implements negative feedbacks maintaining global conditions beneficial to life
    • Doolittle and Dawkins: why would the participants in the biosphere do that, rather than having a tragedy of the commons?
    • Lovelock and Watson's response: Daisyworld models
    • Daisyworld is vulnerable to evolutionary challenge - why would the world be like that and how easy would it be for a "free rider" to invade
    • Sequential selection provides an answer, why biospheres with negative feedback regulation and without free riders are more likely.
  • This is where Maturana and Varela go.
    • Except it isn't, because this is where I want to finish up the Complex Systems lecture from a few weeks ago

Complex systems

  • I won't get to all these things, but I'll put them here for reference
  • emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. (wikipedia)
  • CA
    • 1-dimensional CAs have 4 classes of behavior: equilibrium, periodic, chaotic and "edge of chaos" or complex behavior
    • Conway's Game of Life
      • if alive, 2 or 3 live neighbors to stay alive
      • if not alive, 3 live neighbors to come to life
      • video - some configurations are open-ended, some aren't
    • back to Chris Langton
      • CA and the "edge of chaos"
      • Is there a phase transition between order and chaos? And is there self-organization or evolution to the edge of chaos? Per Bak's self-organized criticality for example.
  • Artificial life
    • Langton CA self-replication:
    • Tom Ray?
    • aside: Grey Walter version
      • 'At the end of an essay on cybernetics that Grey wrote in Colin Ward's Anarchy #25, 1963, (one shilling and sixpence), and which lies here open in front of me, he concluded: "we find no boss in the brain, no oligarchic ganglion, or glandular Big Brother...If we must identify biological and political systems our own brains would seem to illustrate the capacity and limitations of an anarcho-syndicalist community."'
    • contemporary version (Venter, synthetic biology)
    • genetic algorithm
      • Darwin = patron saint of SFI?
      • evolving CA
      • classifier system
    • Fontana's autocatalytic networks
      • origin of life; economics, ecosystems, industry, computing, culture/science
      • diffusion into the adjacent possible
      • Rosetta Stone for Connectionism
        • neural nets, classifier systems, immune networks, autocatalytic reaction networks (and others)
      • all at edge of chaos?
      • Immune system information processing
        • designing an immune system for computers
  • ants + swarm intelligence
    • Ants vs. neural networks
  • sandpile
    • has been used to describe economics, puctuated equilibrium, cancer, political/social change, scientific paradigm shifts, climate change
    • self-organized criticality - solid/liquid phase transition; self-organization to edge of chaos
  • mention Scott Page's nice result - we'll talk about it more in the Democracy lecture
  • SFI researchers published an important result in HIV research at one point - what was it?
  • Agent-based models in ecology and social sciences

To do

  • Give people a report on their midterms grades situation
  • Review of where we've been so far
  • Write M+V lecture
  • New plan for projects schedule, now that we've switched to doing 2 smaller projects in the second half
  • Collect some good videos about complex systems examples or at least illustrations
  • A handout of project ideas
  • Homework - comprehension questions about reading + lecture rather than math work. I will ask students to present their answers (randomly) next time.
  • Reading?

Complex systems unit

Nov. 3: Networks and distributed action

Complex systems II: Networks and distributed action.

How we connect to each other, and some of the consequences. Using some statistics and introducing some set theory and graph theory.

  • General discussion from last week.
  • Get people's answers from last week's homework questions, hand out the new ones. (odt, pdf)

→ Proposals for second project due. Talk to me about them at break.

This week's lecture: Networks and graphs

  • Networks have been the symbol of complex systems since the beginning of system theory in the 1940s or before. Now that we have easy access to computers we can study them effectively.
    • As I have mentioned before, a curious thing about mathematical models is that when a model become popularly known, the main take-away message is often not the conclusions of the model but its assumptions. (And this has clear implications in understanding how math can be used in service of propaganda.) For instance, the most influential message of classical economics is not that supply and demand balance each other, but that people are self-interested; the most influential message of game theoretical models of cooperation is not that defection is the prediction unless there is reciprocity, kin selection or various other things, but that cooperation is hard because of temptation to defect - that's an assumption of the models; and with networks it's not that degree distribution matters, or that there are special positions in a network, but that it's possible to be organized in a way that doesn't have a central position of "power over".
      • Though, of course, a centralized, hierarchical form is one kind of network structure - it's just not the only kind.
      • Classifying structure intro 3 categories: centralized, decentralized and distributed. These are relative terms - how you describe a particular system depends on what you're comparing it with. One network or organization is more decentralized or more distributed than another.
    • So we often hear "network" used to talk about something that is decentralized or distributed, like a coalition or other leaderless organization.
    • Or used to refer to something that uses the Internet, which is the most conspicuous network in our lives presently.
    • Social networks have always existed, but now online social networks are an important part of our daily lives, and there's a lot of debate about whether they're changing the landscape of possibilities for social and political change.
    • There's also the horizontal structure of many social movements, i.e. leaderless. Horizontal vs. vertical. Again, these are relative terms, and there are degrees of horizontal and vertical. (The idea of the tyranny of structurelessness relates to this.)
    • It seems like horizontal structures are becoming more popular, even expected. In social movements there is sometimes a lot of tension between horizontalists and verticalists - for example:
      At the time I was only vaguely aware of the background: that a month before, the Canadian magazine Adbusters had put out the call to “Occupy Wall Street”, but had really just floated the idea on the internet, along with some very compelling graphics, to see if it would take hold; that a local anti-budget cut coalition top-heavy with NGOs, unions, and socialist groups had tried to take possession of the process and called for a “General Assembly” at Bowling Green. The title proved extremely misleading. When I arrived, I found the event had been effectively taken over by a veteran protest group called the Worker’s World Party, most famous for having patched together ANSWER one of the two great anti-war coalitions, back in 2003. They had already set up their banners, megaphones, and were making speeches—after which, someone explained, they were planning on leading the 80-odd assembled people in a march past the Stock Exchange itself.
      The usual reaction to this sort of thing is a kind of cynical, bitter resignation. “I wish they at least wouldn’t advertise a ‘General Assembly’ if they’re not actually going to hold one.” Actually, I think I actually said that, or something slightly less polite, to one of the organizers, a disturbingly large man, who immediately remarked, “well, fine. Why don’t you leave?”
      But as I paced about the Green, I noticed something. To adopt activist parlance: this wasn’t really a crowds of verticals—that is, the sort of people whose idea of political action is to march around with signs under the control of one or another top-down protest movement. They were mostly pretty obviously horizontals: people more sympathetic with anarchist principles of organization, non-hierarchical forms of direct democracy, and direct action. I quickly spotted at least one Wobbly, a young Korean activist I remembered from some Food Not Bomb event, some college students wearing Zapatista paraphernalia, a Spanish couple who’d been involved with the indignados in Madrid… I found my Greek friends, an American I knew from street battles in Quebec during the Summit of the Americas in 2001, now turned labor organizer in Manhattan, a Japanese activist intellectual I’d known for years… My Greek friend looked at me and I looked at her and we both instantly realized the other was thinking the same thing: “Why are we so complacent? Why is it that every time we see something like this happening, we just mutter things and go home?” – though I think the way we put it was more like, “You know something? Fuck this shit. They advertised a general assembly. Let’s hold one.”
      So we gathered up a few obvious horizontals and formed a circle, and tried to get everyone else to join us. Almost immediately people appeared from the main rally to disrupt it, calling us back with promises that a real democratic forum would soon break out on the podium. We complied. It didn’t happen. My Greek friend made an impassioned speech and was effectively shooed off the stage. There were insults and vituperations. After about an hour of drama, we formed the circle again, and this time, almost everyone abandoned the rally and come over to our side.
    • One fundamental result of living experiments like the Occupy movement is that it does seem possible for leaderless organizational structures to work.
    • 1968, groupuscules, wallerstein again... foucault, deleuze + guattari
  • From here, I think I will use part of this Barabasi talk, and pause it in places to add explanations
    • What is p in creating an Erdos-Renyi random graph
    • What is a URL
    • I talked about distributions a bit, let's spell out what a degree distribution looks like. This is statistics. Make a bar chart of how many of the vertices have degree 0, how many have degree 1, and on up.
    • What is a logarithm? What is a log-log plot? Why does a straight line mean there are important hubs in the network that have a lot of spokes?

Three major ideas from network research

  • The small world phenomenon.
    • The Milgram experiment (the small world one, not the fascism one), "six degrees of separation", Kevin Bacon - as in the Barabasi video
    • a small-world network has clustering (friends of friends know each other) and short paths between most points.
    • Two main ways to get one: a localized graph with bridges added, or a scale-free graph.
    • The "strength of weak ties".
      • The less-conspicuous relationships, the ones that aren't active most of the time, and are easily forgotten, can be the most important ones in getting a job, or otherwise making things happen. May be related to the bridge links that make a localized, provincial network into a small-world network. These links are a kind of social capital.
      • If they are related to bridge links in small-world networks, then creating and maintaining them isn't only self-serving, it's also for the common good, because they make it easier for something good to spread across the network and increase potentially fruitful or transformative encounters between disjoint communities.
  • Power-law graphs.
    • Airline network vs. highway network.
    • When there are hubs, you need to deal with the network differently.
    • Hubs are influential: use them to get something to happen; they are weak points if one wants to interrupt something that is happening in a network (disrupt an opponent's organization; stop the spread of a disease).
  • Structural holes
    • If you are in the special position of connecting two disjoint communities, you are in a privileged position and can use it to your advantage. You have insider information from one that the other doesn't yet have (in both directions), and can broker that information or use it yourself. This is a form of structural power.
  • example: Lieberman/Nowak and my work on centralization and consensus
    • illustrates models of something happening on a network; a model that is for multiple things at once; how these models are used to support fundamentally political arguments


To do

  • Record the points on the homeworks I have before I hand them back
  • Write this week's homework
  • Download the Barabasi video so I don't have to worry about network performance while showing it


Nov. 10: Swarms, crowds, and leaderless social movements

Complex systems III: Swarms, crowds, and leaderless social movements.

More on leaderless groups and what they can do. More models.

  • return old homeworks
  • collect incoming hw, ask people's answers in class
  • hand out new hw (odt, pdf)
  • The idea of a swarm
    • read from Multitude, passage about insects? Or the similar piece in We Are Everywhere?
    • (as an aside) find "Insects police state" paper?
  • Swarms in science and similar endeavors
    • videos of starling murmurations: [2] [3] and fish: [4]
    • swarming a classic example of emergence.
    • We've talked about ants. Bees swarm when they need to establish a new hive.
    • Couzin, after working on how birds, fish, and insects respond to each other's movements while swarming, is apparently working on cancer cells that pick up and move to somewhere else in the body together.
    • Craig Reynolds's "Boids" a breakthrough in simulation. Demonstrates that complex, realistic-looking flocking behavior can be produced by many simulated birds with very simple rules of behavior.
      • Reynolds' three "steering behaviors":
        1. Separation: steer to avoid crowding local flockmates
        2. Alignment: steer towards the average heading of local flockmates
        3. Cohesion: steer to move toward the average position of local flockmates
      • video: Reynolds's obstacle avoidance demo from here; [5]; [6]
    • Quorum sensing in bacteria.
    • Life of slime molds
      1. spore single amoeba. Eats and divides, for about 2 days.
      2. starvation stream together, aggregate into sausage-shaped "slug"
      3. Has front and back, is encased in slime layer, crawls toward light, warmth, etc.
      4. Comes to stopping place, raises up into air, changes into a fruiting body, with dead stalk and spores at tip.
      • Video: [7]
      • Note evolution-of-cooperation issues: slug acts like an organism in that anterior cells "sacrifice themselves" to form stalk while other cells become spores and create the next generation.
  • Is swarming an effective way of getting things done, alternative to central planning or leadership? What kind of things?
  • Literal swarming, as a way of moving and occupying space
    • Very hard to defend against. Swarm keeps moving, comes in from many directions at once, can melt away and evade you.
    • Example: Ants and mosquitos are hard to defend against.
    • Example: Military swarming, similar to guerrilla warfare. Approach the target from many sides, cut off lines of supply and retreat, or overwhelm their defenses to enter their territory. Has apparently been important historically in Afghanistan? Some connection between Iraq's current insurgency and these ideas? Swarming robots as well as people.
      • pulsing - attacking here, then there; or now and then. (it's hard to sustain a swarming attack, partly because of loss of surprise, sometimes because of logistics as well - no supply chain, so retreat and return another time.)
    • Example: The Seattle WTO protest. Combination of stationary blockades, swirling crowds overwhelm capacity of officials to get delegates in and out of the ministerial site. Detailed analysis in Networks and Netwars book.
    • Example: Flash mobs. Can be pre-planned, or called/dispatched at last minute using cellphones or internet.
  • Not-so-literal swarming - coming at something from dispersed origins, coordinating in distributed way, but not in geographical space
    • Example: on the internet
      • Distributed Denial-of-service attacks on websites: people (or coordinated computers) around the world access a site all at once, overwhelm its capacity. Used in "hacktivism" increasingly.
      • Anonymous (the hacker activist group) generally acts as a swarm on the internet, making decisions together and carrying them out while cloaked behind anonymous pseudonyms and concealed locations.
    • Example: science, the arts, other kinds of innovation
      • Lots of people have similar but not identical goals: to understand how elementary particles work; to create music that evokes a good response in people; they converge on a number of parallel destinations - in the world of ways to solve a problem - from different directions, while responding to each other, sometimes following, sometimes leading, but trying not to occupy exactly the same space
      • People have used Reynolds-style swarming/flocking models for swarming search in a complex landscape; searching for clusters in large collections of spatial data; "ant colony optimization"...
  • John Robb's formulations
    • Elements of an "open source insurgency" or "open source protest" [8]
      • Plausible promise: An simple goal that people can get behind, that you can believably offer
      • Open invitation: you don't have to agree on everything, just on what we are doing
      • Many leaders: let everyone innovate, do multiple things at once. Support anyone in a leadership role that either a) grows the movement or b) advances the movement closer to its goal. Oppose (ignore) anybody that proposes a larger, more complex agenda or those that claim ownership over the movement.
      • Open source: If a new technique works, document it, use it again, and share it with everyone else. Copy everything that works.
      • Spread the word of the movement as widely as possible.
    • He applies this framework to Arab Spring-influenced movements as well as to Latin American Narco-organizations, free software communities, Al Qaeda and the Iraq insurgency, his "open source venture", potential strategies for the Pentagon, and, he hopes, creation of decentralized "resilient communities" to weather and mitigate the anticipated collapses of the globalized economy and national governments' power.
  • Compare and contrast to World Social Forums and "movement of movements"; neoliberal globalization, the WTO, World Economic Forum; anarchist, communist aspirations; global alliances among commoners [9]; "P2P movements" [10]
    • Note, this sort of thing can be very effective for opposing something but doesn't address the question of what to do if you actually defeat them: "One Yes, Many Nos". For example, what replaces Mubarak? Similarly, if the Occupy movement continues to grow in the US it could force officials out of office (Oakland's Mayor Quan is a likely victim at this point), but what would take their place? More officials? Possibly even people more opposed to the movement's goals.
  • Example: The Arab Spring and Occupy movement.
    • what about them, exactly. fill in. aggregating in one place; decentralized coordination, each locale autonomous; emergent order within each occupation, in formal decision making, self-organization of camp operations, negotiation of goals and coexistence of multiple directions; individuals' courage and self-sacrifice; ...


  • Swarming interlude from Hardt and Negri's Multitude (pp. 91-93).
  • Robb: [11]


to do:

  • grade last week's homeworks
  • write hw questions for this week (odt, pdf)
  • print the reading
  • download and set up the videos
  • visually-oriented project ideas

Nov. 17: Ecology and Permaculture

Complex systems IV: Ecology and Permaculture.

How natural communities work. Ecological models, population dynamics.

  • Collect homeworks. Last week I announced I wouldn't be accepting them late any more, so now I collect all past homeworks.
  • Questions and comments.
  • Go over hw questions from last week.

→ Second project due.

  • everybody present your projects!
  • I'll present my RocketHub project video and statement

→ Informal proposal for final project due.

  • this may be difficult because I forgot to make a point of mentioning this last time. Unfortunately the final project presentations will be in three weeks and our next meeting is in two weeks because of the holiday. So I'll offer my contact info and students can talk with me between classes if they aren't ready to talk about it now.
  • hand out project suggestions (odt, pdf)

Mini lecture about ecology and permaculture


  • Ecology greek roots - how the home works - Oikos is root of both "ecology" and "economics"
  • Concerned with communities - meaningful both literally and figuratively
  • Hierarchy of levels
    • genes - cells - organisms - populations/species - communities - ecosystems - biosphere
    • "panarchy" - i.e. the governance of these systems is emergent and not hierarchical
  • Energy flows through ecosystems
    • energy orientation vs circuit, the causal relationships between things - more cybernetic
  • Gause's exclusion experiment - idea of the niche.
    • But niches are slippery, often exist in relation to other creatures. For instance, birds' niches are sometimes different parts of a given tree, or the same part of the tree at different times of day. How many niches are there potentially in an unoccupied piece of "habitat"? Who knows?
  • Succession - the predictable progression of stages of a community: disturbance - quick opportunists - slower, larger settlers - ultimately to "climax community", or not...
    • succession is a general pattern, happens in forests, lakes, at the bottom of the ocean etc.
  • Competition
  • Predation, also parasitism
  • Mutualism and symbiosis
  • Food webs and food chains
  • Keystone species
  • Invasive species, natives vs. exotics
  • extinction
  • effects of climate change


  • Mollison has described permaculture as "a philosophy of working with, rather than against nature; of protracted and thoughtful observation rather than protracted and thoughtless labor; and of looking at plants and animals in all their functions, rather than treating any area as a single project system." [ wikipedia:Permaculture ]
  • brief video
  • permaculture is a kind of design of whole systems, I think
  • go over the 12 design principles and major patterns from the wikipedia page
  • applying understanding of systems, not just seeking to understand and analyze them
  • something from Lao Tzu? Understanding and then taking action without waste?

To do

No class Nov. 24

Dec. 1: Collective Intelligence and Democracy

Complex systems V: Collective Intelligence and Democracy.

  • Galton's story
    • 800 amateurs placing wagers on the weight of an ox; average of all wagers matched actual weight within 500 grams, while most of the wagers themselves were much further off.
  • Collective intelligence is what?
  • Collective decision making
    • Bacterial quorum sensing
    • collective decision making in animals
      • consensus decision = one that all will abide by, not nec. one that all contribute to
      • vs. combined decision = one made by each individual separately
      • sometimes involves a conflict of interest (resting vs. relocating), sometimes not (choosing site for a new hive)
      • Global vs. local communication? Global (all-to-all) allows for rich negotiation behaviors, local more likely to lead to emergent swarm-style effects of individuals' simple behaviors.
      • What kind of communication? Chemicals, dances, body language, vocal calls
      • Who makes the decisions? All, some, or just one
  • Couzin's model [12]
    • model animals or humans follow a simple swarming rule, to maintain cohesion and separation. Some ("leaders") have a directional preference.
    • A small number of "leaders" can steer the group. More leaders leads to more accurate group navigation.
    • If leaders disagree, the larger group of them prevails.
    • When equal numbers of "leaders" try for two conflicting directions, if the angle is less than 120, the group goes somewhere in between the two directions, while if it's more, one or the other direction is chosen.
    • These predictions have been supported by experiments with homing pigeons and humans.
    • This is coordination - makes the point that coordination can be collective decision-making.
  • people think, learn, make decisions together all the time.
    • as simple as having a conversation or walking together.
    • Science, art, architecture, clothing etc. - all of culture is a results of collective coordination, learning, and creativity.
    • Science is an interesting example - there are carefully maintained practices of peer review, citations, mentoring and certification - yet simultaneously it's fundamentally anarchic - it's understood that no one can manage exactly what scholars will study and where it will take them... a voyage of exploration
      • free software is similar to science
      • crowdsourcing is similar in some ways: Wikis, collaborative bookmarking, collective journalism via Twitter
    • Markets are a way in which people make decisions together, indirectly
    • Maybe mention Graeber's thing here - see notes, below.
    • And then there's governance. How management decisions for a whole society are made.
      • Can be informal - in many small, traditional communities - or very formal. Distributed, decentralized or centralized. We have a mix of different kinds of governance - notice that while global politics is dominated by centralized nation-states, there is no governing body regulating relations between the nations - it's anarchy on the top level. Though there are certainly centers of power on that level, some of which are governments and some of which are private concerns.
    • Social norms
      • Let R be a behavioral regularity in population P. Then more generally, R is a social norm if and only if R depends on the beliefs and preferences of the members of P in the following way:
      • 1: Almost every member of P prefers to conform to R on the condition that almost everyone else conforms, too.
      • 2: Almost every member of P believes that almost every other member of P conforms to R.
      • Bicchieri, "Learning to Cooperate" in The Dynamics of Norms
      • Norms of equity vs. equality
        • Equality: everybody gets the same, regardless of their needs
        • Equity: some get more than others in order to be fair, because they have different needs
      • thresholds, cascades, tipping points
  • Democracy
    • = system in which all have equal share of decision-making power
    • often, equal right to vote in a majority rule process.
    • Prehistoric democracy, likely, was face-to-face discussions in small communities - as Graeber says, if you don't have a police force to make people obey, making decision that everyone buys into is pretty much the only option
    • Athens: restricted to second-generation-native free men. Officials were chosen by lot, except for military generals and treasurers.
    • Rome: republic - two consuls, a Senate (upper house) and assembly (lower house). Senate was aristocrats and more powerful than the assembly.
    • US is a republic similar to Rome. May have been influenced also by the Iroquois Federation - the historical evidence is contested.
    • Contemporary social movements favor consensus and similar forms of horizontal direct democracy, conspicuously the Occupy movement and its precursors in Spain and Greece (not to be tiresomely repetitive)
  • There are a lot of ways to vote
    • Simple majority vote. If there are more than 3 options, there might need to be a runoff.
    • Instant runoff voting (aka preferential voting), as in San Francisco and Oakland.
      • Each voter makes several ranked choices, say 1st, 2nd and 3rd choice. Count all 1st choice votes to choose a winner. If there's no majority choice, eliminate the candidate in last place and replace all votes for that candidate by the 2nd choices. Continue this pattern until a winner has the majority.
    • Condorcet's Jury theorem
      • recalls the Galton result: if each person on the jury is error-prone but their votes approximate the right answer, then the larger the jury is the more likely it'll choose the right answer by majority vote.
    • When there are more than two choices, the situation falls apart: a "perfect voting system" is impossible. This is largely because of "rock-paper-scissors" situations where preferences are tangled and contradictory ("intransitive").
      • Arrow's three criteria:
        • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
        • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
        • There is no "dictator": no single voter possesses the power to always determine the group's preference.
        • Arrow's Impossibility Theorem: No voting rule can satisfy all three of these.
      • Gibbard-Satterthwaite theorem is also relevant: given three or more candidates:
        1. The rule is dictatorial (i.e., there is a single individual who can choose the winner), or
        2. There is some candidate who can never win, under the rule, or
        3. The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his preferences.
  • Procedures for deliberation is a bit different from voting systems.
    • Parliamentary procedure is very formalized - Robert's rules of order is a famous version
      • Introduce a motion
      • Rules for debate, who gets to speak when
      • Amendments, seconds; vote, table, or postpone.
        • Voting is often by majority, counted informally.
    • formal consensus
      • Similar to parliamentary procedure but with important differences.
      • Proposal, concerns, friendly amendments, blocks, consensus.
      • Key difference is adoption by consensus rather than majority vote.
      • Changes the whole approach from winning numerical support to working together, addressing concerns, getting buy-in. Advocates say it avoids "tyranny of the majority".
      • Can be slow, aggravating; larger groups often adopt supermajority rules instead of pure consensus, largely because they need to make decisions within a time limit even if there is some discord.
    • Story circle process? Open Space Technology? Dynamic Facilitation... there are lots of innovative processes out there
  • Power
    • Habermas's ideal speech situation:
      • 1. Every subject with the competence to speak and act is allowed to take part in a discourse.
      • 2a. Everyone is allowed to question any assertion whatever.
      • 2b. Everyone is allowed to introduce any assertion whatever into the discourse.
      • 2c. Everyone is allowed to express his attitudes, desires and needs.
      • 3. No speaker may be prevented, by internal or external coercion, from exercising his rights as laid down in (1) and (2).
      • This is not a deliberation process, or a voting scheme; it's preconditions for a discussion leading to "truth", whatever form the discussion may take. Note these preconditions are generally not satisfied here in the world.
    • Tyranny of structurelessness argument.
    • Potential conflicts between independent action, consensus. When is it necessary to get others' consent before acting?
      • examples: science, technology. "liberation technology". my essay on this.
  • scott page's model, which is kind of awesome.
    • there is a "problem space", which is an abstraction that takes the place of whatever actual problem people might want to solve together.
    • a proposal is a point in the problem space.
    • different people have different heuristics for problem solving, that is, when a proposal isn't satisfactory, how to come up with a new proposal. They go from the current point in the space to various "nearby" points, but different ones than other people do.
    • result: this diversity in ways of solving problems makes the group way more effective at finding a satisfactory solution than if everyone is the same. Even a little diversity makes a huge difference. This happens because the diversity makes it much less likely that the group will get stuck on a proposal that isn't good, but doesn't have any better possibilities "nearby".
  • my current project, briefly.
    • Similar structure to Page's: looking for a good point in a problem space.
    • Difference: different people have different opinions about which solutions are good, not just about how to look for good ones.
    • Ask questions about how to look for something that satisfies all the people well enough. Different deliberation processes, voting processes, rhythms of communication.


Things that don't exactly fit but I wish they did

  • Changing the word from "occupy" to "decolonize". What is decolonization.
  • Graeber's schema, in Debt: The First 5,000 Years: there are 3 modes of human interaction - communistic sharing; exchange; hierarchy. Debt is in the exchange mode, and we get very uncomfortable when it's applied to things that belong in the other modes.
    • Note, also: Graeber is going to give a lecture here at SFAI on Jan. 27. Be sure to mention to class.


Dec. 8: Final project presentations

Final project presentations.

  • Maybe a brief review of what we did all semester.
  • Students present their projects.
    • Research on how video feedback works, and maybe show a video feedback experiment from last time around that didn't get shown.
    • Potentially, a video-feedback reinterpretation of DeFeo's The Rose
    • Experimental random video that I tried to screen last time, but the software didn't work.
    • An investigation of bacterial quorum sensing and behavior of Critical Mass riders
    • One I can't remember right now
    • One who didn't tell me what they're going to do
    • I hope to present something about Qi Gong and internal martial arts in general from a perspective of treating the self as a system
  • I promised cookies.


  • Make cookies
  • Call facilities, get a Mac for showing videos because my laptop stumbles on Quicktime videos sometimes.
  • Qi Gong project.
  • Return all graded homeworks.
  • Turn in final grades.
  • Find out when grades are really due, in case students ask for an extension.


  • No DeFeo, sadly, but a nice colored-pencil drawing based on the motion of flocking starlings
  • A very entertaining experimental video (from the second project, actually, but the video projection didn't work right so we saw it now)
  • A written investigation of how video feedback works. It was sufficient, but didn't hit all the places I would like for a really good grade. But then I heard the student explaining it a bit in class and I was satisfied that they did understand the basics about circular amplification, so I upped the grade.
  • A report on collective dynamics, with some interesting points about locusts that I didn't know and apt comparisons between how it works in insects and in people (birds migrating, bicyclists racing; locusts; participation and herding on the dance floor)
  • A report on swarms submitted in absentia by a student who left town. Some good research there as well.
  • Cookies turned out good. Apple cider, soda water. People didn't eat all that much of it, so I got to keep the rest.
  • I was very busy this week and ended up very sleepy, so I didn't do a presentation on Qi Gong, sadly. I let us all go home early since we were done.

Project Ideas

For the first project

  • The regular kind of musical feedback is easy, with a guitar or microphone. Come up with another kind of musical feedback (whether positive or negative) and investigate it. Or something original to do with video feedback or some other kind of feedback.
  • Consider a situation that interests you, whether a political process, a family pattern, the classroom, something else at SFAI, traffic jams, an artistic process, or something else, and discuss the feedback processes that you see in play. Or build a mathematical model or a computer model...
  • Investigate some more involved mathematical models than we have done in class, and report what you learn.
  • Invent a new game, where the rules seem simple but produce some interesting behavior when you play.
  • Build one of the systems or projects we've discussed in class into a 3-D or other interpretation that has something of interest to it.
  • Investigate Norbert Wiener, Ralph Abraham, Stewart Brand, or one of the other people or groups we've mentioned and report what you learn.
  • Find out where my cell phone has been located in recent months, and plot my trajectory on a map. (Don't reveal any kind of illegal activity to me because I might be required to report it.)
  • Investigate one of the ideas we've talked about in more detail. Computer modeling, cyberneticists' machines, 60s communes and self-organization, chaos, ...
  • Create a rule-based or generative art project. Could be music, performance, a visual medium, a computer experiment, whatever. The rules should lead to something interesting that isn't obvious from the rules themselves.
  • Create a system that does something interesting. Or design it and tell us about it without actually building it.
  • Identify an existing system and think about ways to perturb it. Try it and see what happens, or discuss what you think would happen and how you would get particular desired results.
  • Identify an existing system and think about ways it could be organized differently. What would be the consequences?
  • Other project ideas are welcome. These are only suggestions.

Project 1 ideas handout: odt, pdf

For the second project

  • Use ideas from Donella Meadows's Ways to Intervene in a System to think about ways to intervene in some system that interests you.
  • Use Peter Taylor's ideas about how to think critically about a tragedy of the commons or other system model, to question a system that interests you, or to challenge claims about a system.
  • Criticize something from the readings, lectures, or videos that you disagree with.
  • Do an experiment relating to cooperation and selfishness, to find out what people do when you put them in a certain situation. Discuss the experiment in terms of the game theory ideas from the reading, or the tragedy of the commons, or something related.
  • Learn more about natural selection and make a report. This could be about biology and evolution, or about culture, fashion, art, social change, or something related.
  • Investigate what processes the Occupy Wall Street movements (Occupy SF, Occupy SFAI, etc) are using to organize themselves, coordinate, and communicate with the public. They have working groups, formal consensus decision making process, electronic communication via Twitter, etc.
  • Do some more of what you did in the first project.
  • The suggestions for the first project are still available.

Project 2 ideas handout: odt, pdf

For the final project

  • Building on the Steven Johnson reading, investigate one or two online communities or social networks and how they are designed to get certain kinds of interaction to happen.
  • Swarms of birds, fish, or insects. What they look like, how they move. How the swarm comes from the individuals' movements.
  • Swarms in the Occupy movement. The recent demonstration at the Port of Oakland, or the really recent one at the New York Stock Exchange. How the action of the crowd comes from the individuals' actions. Or the back-and-forth between eviction of the camps and re-occupying the space, how that emerges from individuals' actions.
  • Learn more about ecology or permaculture. Or something about learning another system well and knowing how to take action without waste: taking care of your body, or being part of a community or family; or sports or martial arts, or making money, or knowing an artistic medium or craft well. (Connect this to the idea of a system and understanding how the system works.)
  • The characteristics of an "open source insurgency" or "open source movement": apply this scheme to something different from the examples I used in class, and see whether it fits or not. Discuss why or why not.
  • The suggestions for the first and second project are still available.

Final Project ideas handout: odt, pdf

Overall postmortem

If I get to do it again, I would like to. I would improve the structure of the semester, improve the math part at the beginning and look for a way to distribute the more formal math more evenly across the semester. I'd refine the homeworks, and bring in better multimedia presentations and activities. Especially, I'd focus on the teacher/student interaction, and since the meat of the lectures is written I would pay much more attention to going beyond the one-way lecture format to involving the students more in the process, maybe having them learn and present some of the material, teach each other, more activities and hands-on projects. I would also pay sustained attention to the process when I'm lecturing, how to question the students, ways to engage them and assess what they are and aren't getting.

The grading worked out pretty well - I found effective ways to reward a reasonable amount of effort in a challenging subject with good grades while still grading with integrity, not giving patronizing good grades to shoddy work. Still, I might be more stringent next time.

It would probably be very good to be more concrete about exactly how grades will be assigned and make sure students know. Not only how many points each assignment is worth and how points will translate into final grades, but also how they will be graded, particularly what criteria I use to grade projects. If students are trying to guess what is a high-graded project, I end up putting myself in a bind where I don't want to grade them low for guessing wrong, but if I don't grade them low I'm not really requiring them to engage with the material.

General Notes

  • look through other course descriptions, activism, urban studies etc, look for overlapping interests
  • for next time, consider reframing as 'an exploration of math in society'?

  • long-term behavior of simple systems. equilibrium, cycles, etc.
    • equilibrium = limit
  • stability: stable = bowl, unstable = hilltop
    • pendulum at top/bottom of swing
    • stability to perturbation, that is
  • more on states, trajectories, graphing, models, variables, algebra
  • thermostat model (first nonlinear example?)
  • begin to talk about feedbacks. negative feedback, positive feedback, combinations of them. history, cybernetics.
    • invisible hand = negative feedback? economics; ecology, evolution
    • positive feedback, change. autocatalysis
  • what simple dynamics can do - linear and nonlinear
  • circuits, more complex models
    • causal loops karma?
    • John Muir: "When one tugs at a single thing in nature he finds it hitched to the rest of the universe"
    • consider Joanna Macy book on Mutually Dependent Co-arising
    • sign of a feedback = product of signs around the loop? (cf. qualitative loop analysis)
  • cybernetics, the history.
    • feedback, regulation, purpose, learning
    • Bateson; symmetric and antisymmetric interactions; addiction; mind and nature
    • run through Maturana and Varela's ideas, maybe
    • systems, gaia
    • Cybernetics and 60s experimentation... feedback, psychedelics, self-organization, psychology...
  • talk about "rules" and emergence. "Laws" of nature.
  • systems and politics. systems vs "The System". Wallerstein, Marxism, ...
  • Prigogine, open systems, bifurcation points, thresholds + decision making
  • Modeling. what is a model. simulation. science studies again.
  • discrete maps.
    May's chaotic map?
    • autocatalytic = positive feedback. increasing returns economics. the machinic phylum.
  • society of control
  • Larry Richards, time, conversation and politics (probably not, though)
  • something about School for Designing a Society and composition and performance?
  • group process, story circles etc.
  • something to do with Nonlinear
  • the dream of the systempunkt. Fuller's "trimtabs".
  • von Foerster, design, ethics and degrees of freedom. my paper on degrees of freedom.

  • create concrete lists of goals
    • specific goals for week's lesson plans (adding fractions or whatever)
    • larger goals for longer term (recognizing a system/model, equilibrium)
    • plan the whole course with end in mind: what want students to do at end of course.
      • (and what do they know at the beginning)
  • focus on which 80%? The bottom, middle, or top?
  • keep students up to date about their grades
    • midterm feedback: what I gave you, why, how to improve for final grade
  • reading maybe much more important than lectures - what they keep
    • physics guy in Conversations with Great Teachers - have them do the reading, send you their questions, spend class time on their questions
  • homework? drill + essay questions?
    • optional questions for more advanced students? easier, more interesting, to attract them
  • show more than one way to prove things.
  • Math and visual art
    • perspective
    • cubism? impressionism?
    • architecture
      • vernacular architecture; pattern languages; african fractals
    • symmetry
      • abstract algebra, groups
      • printmaking? positive/negative (... John Cage)
    • physics of color
    • Islamic tilings (Saira has books)
    • polyominoes, Penrose tilings
    • computer graphics
  • Music and math?
    • ratios, harmonies, rhythms
    • Pythagoreans, scales
    • Randomness and 20th century music; tone rows; ?
    • deleuze/guattari and music? ambient sound? noise music?
    • Emily Doolittle, animals' music (maybe not)
    • poetry, meter
  • Algorithms
    • how to understand computers, the internet, electronically mediated life through idea of algorithms
    • do some in class
  • Information + Bits
    • reliable transmission, alphabet size
    • writing systems
      • Iraq/cuneiform
      • see also, numerals, numbering systems
  • ancient engineering
    • rice paddies, water temples
  • permaculture
    • transport networks (?)
  • conceptual art?
  • dance?
    • cage + cunningham...
    • esther williams, lol
  • Numbers, arithmetic
  • Logic, proof
    • Euclid's proof of no largest prime (requires multiplication, factors, proof)
  • Algebra and variables
    • Karl Marx's algebra?
  • How to read science news stories critically
    • lying with statistics (and some review of basic statistics concepts)
  • Fashion? Design? Online creation and publication? Digital music? Computer animation?