Posts Tagged ‘design’
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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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!
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.
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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The interrelationships between society and technology run deep. We all partake and participate in the unfolding technology evolution “discussion” that is our lives. The tools we use, try out, improvise, critique, and/or advocate are our minimal contributions to this discussion. The accidents of technological history set the context for the discussion. We are all technologists entangled in a technological world! Technology has been the main (perhaps the only?) means by which human progress has been achieved with tools like the pencil, slide fastener (or zipper), jet airplane, water systems, skyscrapers, bridges, and computers all dramatically changing society. Henry Petroski’s great short book “Invention by Design: How Engineers Get from Thought to Thing” explores the design and engineering arts in the full richness of their social context in nine intriguing case studies.
I first read Invention by Design in February 1999. Recently I was re-reading it when Michael Tweed of the The Ben Franklin Thinking Society invited me to lead the group’s Science & Technology meetup every month. That led to the Discussion: Engineering Failures & Society on 8 May 2011. Here are some thoughts reflecting on Petroski’s book, the 8 May meetup, and further cogitating about the big picture of society and technology. Hopefully these notes and your feedback will help us better understand the technological world at the core of our ever changing civilization.
What is Technology?
Petroski’s definition suggests that civilization itself may be technology. So it would seem that technology embraces culture, values, psychology, history, and the multidimensional elements of the environment (materials science, biology, anthropology, geophysics, chemistry, etc.). Buckminster Fuller goes further:
In its complexities of design integrity, the Universe is technology. The technology evolved by man is thus far amateurish compared to the elegance of nonhumanly contrived regeneration. Man does not spontaneously recognize technology other than his own, so he speaks of the rest as something he ignorantly calls nature. — Buckminster Fuller, Synergetics, 172.00-173.00
By taking Petroski’s “networks, systems, and infrastructures” to the next level of “design integrities” and identifying it as technology, Bucky leads us to the biggest of big pictures: Universe itself! As social creatures we often think of society as the big picture. I think his point is well made: technology is an inhernet component of Universe itself. Human society is our storied Earth-developed technology. It seems likely that Human society will become the “brain” managing the regenerative ecological functions of Gaia, the theory that Earth is “alive”. If that happens, the storied technology of Earth would probably become even more syntropic and powerful than what life has achieved thus far. Regardless, society and the technology with which it is built are inextricably intertwined!
Design and Engineering in Society
Design and engineering are the arts of consciously working to evolve and develop our technological infrastructure to improve our worlds. Petroski emphasizes the role of society in the engineering process and vice versa in these illuminating quotes:
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