Mathematics as the Central Principle of Modern Origami

At min 2:00 of his TED talk, Robert Lang asks what has allowed the recent explosion of innovation in the ancient art of origami:

And it raises a question: what changed? And what changed is something you might not have expected in an art, which is math. That is, people applied mathematical principles to the art, to discover the underlying laws. And that leads to a very powerful tool. The secret to productivity in so many fields -- and in origami -- is letting dead people do your work for you. (Laughter) Because what you can do is take your problem, and turn it into a problem that someone else has solved, and use their solutions. And I want to tell you how we did that in origami.

In his excellent talk, Lang refers to modern examples of origami, including a cuckoo clock made from one sheet of paper and no cuts. Lang proceeds to discuss the mathematics of origami. Beautiful, mathematical and mind-blowing. It's an excellent talk with more than a few laughs along the way.

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Daniel Dennett’s Technique for Criticizing a Position

I'm reading Intuition Pumps and Other Tools for Thinking, by Daniel Dennett (2013). This approach for criticizing a claim caught my eye:

How to compose a successful critical commentary:

1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.” 2. You should list any points of agreement (especially if they are not matters of general or widespread agreement). 3. You should mention anything you have learned from your target. 4. Only then are you permitted to say so much as a word of rebuttal or criticism.

One immediate effect of following these rules is that your targets will be a receptive audience for your criticism: you have already shown that you understand their positions as well as they do, and have demonstrated good judgment (you agree with them on some important matters and have even been persuaded by something they said).

This passage is at page 33.

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Research Tools – the Beginning of a Collection

I decided to create a new category today: "Research Tools" I wanted to create a place where I could find interesting places to find things. Here's the first entry, describing seven such places for high quality research: "7 Great Educational Search Engines for Students" It briefly describes the following: 1) Educational Resources Information Center (ERIC) [M]aintained by the U.S. Department of Education. You’ll find more than 1.3 million bibliographic records of articles and online materials . . ." 2) Lexis Web Searches validated legal sites. 3) Google Scholar From Wikipedia: "Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines." 4) Microsoft Academic From MA: "Microsoft Academic understands the meaning of words, it doesn’t just match keywords to content." 5) Wolfram Alpha.   From the website, "he introduction of Wolfram|Alpha defined a fundamentally new paradigm for getting knowledge and answers—not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms and methods." 6) iSeek Education  From the website:  "iSEEK Education is a targeted search engine for students, teachers, administrators, and caregivers." 7) ResearchGate From the website:  "ResearchGate is built by scientists, for scientists.It started when two researchers discovered first-hand that collaborating with a friend or colleague on the other side of the world was no easy task."

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