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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What You Should be Thinking as You Fill Out Your Paperwork at the Doctor’s Office

When you arrive at the doctor's office to check in with the receptionist, you are often handed a small pack of paperwork to fill out. Until that moment, you have probably been focused on your own ailment or your own medical worries. Luckily, for most of us--most of the time--our own health concerns will more or less resolve and life will more or less go on.

For all of us, however, that typical pack of doctor office paperwork contains a magic page that has the power to boost our happiness through the roof, if only we employ the correct frame of gratitude.  I'm referring to the page that looks something like this:

This page gives us the opportunity to breathe a cosmic sigh of relief that we do not have most of those ailments on that list.  That's how I try to see it as I check off all most of those boxes with a "no." Thank goodness I don't have most of those medical problems. And this is merely the beginning of what I'm proposing as a journey of gratitude.

Instead of thinking about my own health problem, instead of being frustrated that my own body is not operating perfectly, the above page is a reminder that my body is an extraordinarily complex adaptive system--lots of little parts have self-organized into something so complicated that it seems miraculous. No humans could possibly make a tongue or an eye or a liver as high functioning or as elegant as the natural versions.

Imagine that humans in the distant future worked very hard and came much closer to making a reasonably functioning robotic human. Then imagine their supervisors sending down a new work order to make sure that this robot is also sentient.  Imaging the groaning you would hear from the engineering team! Then imagine that the supervisors send down another new work order to make sure that this artificial human could also repair itself if it became damaged!  Imaging louder groaning, especially when the supervisors remind the team that this self-repair must respond to hundreds of millions of microscopic threats and do it as well as the human immune system. 

Then imagine that the supervisors send down yet another work order advising the team that they must design their human so that it runs on almost anything that it puts in its mouth.  Even louder groaning.  Mutiny is threatened.

Finally, thousands of years later, when millions more engineers (and their great great great great grand-engineers) have successfully created a passable artificial human, the supervisors call down with one more new request:  Make sure that these artificial humans can create tiny artificial humans the size of a pinpoint that will grow, within the body of one of the robots, into large artificial humans who become wise through their interactions with any of dozens of environments.  Then imagine all the engineers quitting their jobs.

At the doctor's office, our question should not be "Why doesn't my body work perfectly?"  We shouldn't even complain that we sometimes have one or more of those ailments on the long checklist handed to us by the doctor's receptionist. A better question is "How is it possible that the actions of countless individual molecules self-organize into trillions of cells that result in emergent coordinated macroscopic behaviors such as the ability to walk into a doctor's office?"  Even more simply, the first question should always be "How is it possible that human bodies work at all, ever?"

Answer not forthcoming.

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Bellefontaine Cemetery in St. Louis – More than a Cemetery

People in STL call it "Bellefontaine Cemetery" but on its website you'll see this: "Bellefontaine Cemetery is a nonprofit, non-denominational cemetery and arboretum . . ." I know it best as an extraordinary place for getting lost on feng shui inner roads and for reveling at the 5,000 trees. And for reading the 87,000 graves and monuments for the meagre clues they offer about those who used to walk and talk like you and me.

 

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