Harold Channer invited me to the studios of MNN (Manhattan Neighborhood Network) in New York City to record two one-hour editions of the TV program “Conversations with Harold Hudson Channer” on Tuesday the 25th of November, 2014. Since few things I write or speak come out fully baked, I thought I’d add a few additional thoughts to clarify, improve, or correct some of my comments. Since I value discussion, I sprinkled my remarks with many questions which I hope will elicit your feedback in the comments.

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I participated in the ReVIEWING Black Mountain College 4: Looking Forward at Buckminster Fuller’s Legacy conference on September 28-30, 2012 in Asheville, NC, USA. I gave two talks (click on the links below to see the PDF presentations):

• Education Automation Now and in the Future. In this talk I recognize Buckminster Fuller as one of the conceptual founding fathers of the Open Educational Resources (OER) movement, detail six of his educational ideas, and give a brief review of several OER courses I’ve taken to indicate the kind of comprehensive education now possible using freely available on-line courses.
• Synergetics and Model Thinking. In this talk I synthesize Scott E. Page’s Model Thinking with Buckminster Fuller’s Synergetics. I introduce both subjects, then discuss the importance of model thinking. Then I sketch some ideas about how Model Thinking and Synergetics can inform a more incisive approach to science.

Please share any thoughts you might have about these presentations in the comments. I would value your feedback.

The Fano Plane 7₃

For me the most enticing facet of projective geometry is the profound way in which it treats duality. Duality is the notion that certain fundamental distinctions have similar structure in their complementary forms. In comparing a form with its dual, the basic structure remains even though the roles of the forms reverse. Inside and outside. Convex and concave. Yin and yang. In 2D (two-dimensional) projective geometry, point is dual with line; in 3D point is dual with plane while lines are self-dual. The relationship of duality is so penetrating and pervasive in projective geometry, that we might consider it the geometry of fundamental duality. It provides a geometrical stage upon which duality can be studied in a pure form.

Another profound aspect of projective geometry is its elementary treatment of incidence where one considers the join (∨) and meet or intersection (∧) of two basic geometrical objects such as point, line, plane, and hyperplane. The most fundamental correspondence of geometrical forms associates points and lines in dual arrangement: the points on a line form a range and the lines through a point form a pencil. The correspondence between a pencil and a range is a basic projection. Next a perspective relation joins a pencil with two ranges or a range with two pencils; that is, by combining two elementary projections. Such a perspectivity maps points to points, or dually, lines to lines as shown in the figure.

In the essay “Design Strategy” in Buckminster Fuller’s book Utopia or Oblivion, he includes projective geometry in his list of recommendations for a curriculum of design science. The connection between projective geometry and design thinking is an area that deserves more attention.

A Catalog of Models of Projective Geometry

The rest of this essay tersely describes a broad listing of some of the more basic models of projective geometry. Models are a powerful tool for learning and for understanding as explained in my essay about the Importance of Model Thinking (based on Scott E. Page’s course). The models included below should provide an introduction to and an overview of projective geometry for those new to the subject (Note: some of these models require background knowledge that is not explained here. They are indicated with a . I encourage you to skim or skip such models, but to read on as later models may be more tractable.) I hope the experts will find the succinct summary and references useful. Although this list is fairly comprehensive, there are many models that are necessarily omitted. If you have a favorite model, please post a comment about it.

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Models can help us understand, predict, strategize, and re-design our worlds. This is the profound lesson from Scott E. Page’s engaging on-line Coursera offering on Model Thinking. I was particularly interested in this 10 week course because Buckminster Fuller instilled in me a deep appreciation for models. With this course, Scott Page reinforced and enhanced that appreciation in spades. Also, like Bucky, Page makes his penetrating approach accessible to a very broad audience. This is a great course for anyone with even rudimentary algebra skills.

In addition to reviewing the course, I will also suggest that model thinking is a new more incisive kind of science. This approach and its nascent toolkit for understanding, decision-making, prediction, strategy, and design is vitally important for practitioners of all types. Model thinking may be just the type of tool humanity needs to solve some of its thorniest problems. As such its arrival into broader consciousness is not a moment too soon!

So if you want to be out there helping to change the world in useful ways, it’s really really helpful to have some understanding of models.
— Scott E. Page

Why Model Thinking

There are many ways to model the world. One of the most popular is with proverbs or short pithy sayings (our modern media seem to particularly love this deeply flawed “sound bite” approach to knowledge). As Scott Page points out, there are opposite proverbs too. For instance, the opposite of “nothing ventured, nothing gained” is “better safe than sorry.” Proverbs and their more elaborate cousins, allegories, can model or represent the world with persuasive stories, but they provide little discerning power and little basis for deeper understanding. In contradistinction, model thinking with its greater concern for precision can help us more carefully distinguish a complex of important factors with their interrelationships and behaviors. Therein lies its power!

Is intuition sufficient? No! Philip Tetlock, Robyn Dawes and others have demonstrated that simple naive models outperform experts of all stripes. In 1979 Dawes wrote a seminal paper, The Robust Beauty of Improper Linear Models in Decision Making, which showed the effectiveness of even “improper” linear models in outperforming human prognostication. Tetlock has made the most ambitious and extensive study of experts to date and finds that crude extrapolation models outperform humans in every domain he has studied.

That is not to say that models are “right”. Page emphasizes that all models are “wrong” too! Which leads to his most profound insight in the course: you need many types of models to help think through the logic of any given situation. Each model can help check, validate, and build your understanding. This depth of understanding is essential to make better decisions or predictions or build more effective designs or develop more effective strategies to achieve your goals.

Is intuition important? Yes, absolutely! The many model thinker relies upon intuition to select and critically evaluate a battery of models or to construct new or modified models when appropriate. These models help test our intuition. Intuition helps tests the models! Writing out a model often identifies facets and elements of the situation which intuition misses. Intuition is essential to find the aspects of the models that are a bit off the mark — and all models are a bit off. Model thinking is not “flying on instruments” or turning control over to mathematical or computer models. Instead it is about evaluating and comparing diverse models to test, build, fortify, and correct our intuitions, decisions, predictions, designs, and strategies.

Fascinating Models

Page’s course is filled to the brim with fascinating models! One of the first models Page introduces is Thomas Schelling’s segregation model which represents people as agents on a checkerboard. We discover deep and unexpected insights about how people sort themselves into clusters where everyone looks alike, for example, the segregation of neighborhoods based on race, ethnicity, income, etc. It is the first of many agent-based models to be discussed.

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It may be that the presumed dichotomy between determinism and randomness is superficial and illusory. Determinism is the world view that events result from an unalterable causal chain. It models the world as a clock whose behavior can be inferred by scientific investigation. Stocasticity or randomness is the world view that uncertainty pervades experience. It models the world as a dice game with unpredictable behavior.

Many thinkers including Einstein, Buckminster Fuller, and D’Arcy Wentworth Thompson have argued in support of the traditional deterministic world view[1]. However, Quantum mechanics, machine learning, and behavioral economics are three prominent areas which have helped realign modern thinking to apprehend that randomness and uncertainty may be fundamental and pervasive. Leonard Mlodinow in a 2008 book goes further and argues that randomness rules our lives.

In preparing for and discussing randomness at a recent meetup of the Ben Franklin Thinking Society, I started to gravitate to the hypothesis that uncertainty and determinism may be like inside and outside or concave and convex. They may be both real, both partially right and partially wrong, both revelatory and misleading. It may be that each perspective is a “tuning in” to only part of a reality that is both-neither[2].

The principle of functions states that a function can always and only coexist with another function as demonstrated experimentally in all systems as the outside-inside, convex-concave, clockwise-counterclockwise, tension-compression couples.

— R. Buckminster Fuller, Synergetics 226.01

Here are several ways to see the dual and co-occurant qualities of the stochastic and deterministic models or world views.

In a deterministic model of the world, the fixed set of laws that govern everything apply to every quanta of energy or their constituents. So computing the state of the world requires applying these fixed laws to each such quanta from some initial state and iterating through each picosecond of time. Clearly, this is computationally infeasible except for the computer known as Universe itself. So any effective simulation or calculation will entail estimates and approximations, that is, randomness. Unwittingly, randomness imposes itself into the system!

Conversely, in a stochastic model the relationships between data are given by frequencies with respect to their sample space, the set of possible outcomes. What could be more deterministic than the elementary counting of frequencies? Indeed probability is basically a form of advanced counting in ratios. Deterministic indeed!

Now consider measurement. The basis of a scientific model involves measurable parameters. Data are measurements. Science has determined that all measurements involve uncertainty. MIT physicist Walter Lewin puts it emphatically: “any measurement that you make without any knowledge of the uncertainty is meaningless!” Measurement theory is built upon the law of error which is a principle of the science of randomness. Hard data acquires its validity and persuasiveness from the science of chance!

The key to understanding measurement is understanding the nature of the variation in data caused by random error.
— Leonard Mlodinow

On the other hand, the law of error is a central principle in statistics, the science of inferring probabilities from observed data. Such inference is the gold standard of scientific truth. The techniques of scientific inference are based on the mathematics of randomness. Like all mathematics, the theory is definite, rigorous, and repeatably verified by logic, proof and experiment. The sciences of probability and statistics are rigorous and deterministic like all mathematics!

Even in a fundamentally deterministic world, our understanding, decision-making, strategies, predictions, measurements, and designs are predicated upon uncertainty and randomness. To be effective we must be cognizant of these lingering unavoidable uncertainties.

Conversely, even in a fundamentally uncertain world ruled by randomness, pattern and order emerge and can be identified. To be effective we can and should seek the design and structure permeating through the apparent randomness.

From these considerations, I conclude that randomness and determinism always and only coexist. They are inseparable. Each provides a spectacular, incisive perspective on reality. The careful thinker or practitioner should be facile in using both types of models to get a more wholistic, more complete picture of the world in which we find ourselves. This is evidence that both-neither should be our guiding principle in seeking truth!

Do you find the argument compelling? Is it sound? Can you help me improve it? Do you see other ways in which these two models interpenetrate and interaccommodate? How do you see the interrelationship between determinism and randomness?

To better develop my understanding of a more complete set of models (beyond superficial determinism vs. stochasticity), I am excited about Scott E. Page‘s new and just started on-line video course on Model Thinking. I think we need many diverse models to sharpen our thinking and uncover subtleties in the complex systems and theories upon which our civilization is built. I am looking forward to wrapping my head around the 21 or so models in this course. You can register for the Model Thinking course by filling out the form at http://www.modelthinker-class.org/.

So if you want to be out there helping to change the world in useful ways, it’s really really helpful to have some understanding of models.
— Scott E. Page

Finally, here are three good audio-visual resources that explore issues of randomness further:

• Radiolab’s exquisite podcast on Stocasticity.
• World Science Festival: The Illusion of Certainty: Risk, Probability, and Chance.
• Persi Diaconis’ talk “On Coincidences” (scroll down near the bottom where the 1998 lectures live or search for Diaconis).

[1] Click here to read my previous essay on randomness where arguments for determinism are discussed.
[2] Credit to Tom Miller for the wonderful expression both-neither.