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Cover of Stephen Barr's book "Experiments in Topology")

Stephen Barr’s “Experiments in Topology” (originally published in 1964, reprinted in 1989 by Dover) is extraordinary because it treats a sophisticated mathematical subject with accessible language that can be understood by motivated junior high students. It is extraordinary because its wonderful and copious figures are remarkably clear and elucidating. It is extraordinary because it captures the flavor, depth, and breadth of a very subtle subject with carefully written passages that boil down significant complications into understandable overviews. It is extraordinary because he gives a concrete enough treatment that the attentive reader can learn something substantial of the subject while the mysteries that are both alluded to and implicit may drive the curious reader to explore its nooks and crannies. It is extraordinary because its learning-by-doing (experimental / exploring) style is infectious and the reader may be emboldened to ask their own questions and attempt their own experiments. It is extraordinary because its effective survey of key ideas in the major branches of topology make it a useful reference. It is extraordinary because it can reward the casual reader with some basic guideposts for apprehending an advanced subject while the serious student who builds all its models and tries to understand their integrated significance can extract many deeper insights from the text.

I prefer this latter, in-depth, approach and organized, through Math Counts, a mathematics group in Philadelphia, 11 deep explorations on topics from the book each with a group of 6-10 mathematically-oriented colleagues. We thoroughly enjoyed the book and our explorations, although after 11 months we wanted to move on to other ideas.

The book uses homeomorphism as its first principle for exploring topology. Barr gives several definitions, but I found the characterization on page 5 to be the most helpful: “Any distortion is allowed provided the end result is connected in the same way as the original.” This exemplifies the kind of careful but informal style of the book.

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Society and Our Technology Built World

datePosted on 2 June 2011 by cjf

The interrelationships between society and technology run deep. We all partake and participate in the unfolding technology evolution “discussion” Invention by Design by Henry Petroski 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?

Technology is the catch-all term used to describe objects and the networks, systems, and infrastructures in which they are embedded, as well as the patterns of use that we impose upon them and they upon us. Technology is clearly context-dependent and ever evolving. — Henry Petroski

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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