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LL Pete
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Order in Chaos

That's what Taffgoch, the creator of this picture, calls it.  It's a computer-generated image, made to look nicely weathered... but it's based on an actual model, made by a monk named Father Magnus Wenninger.

Wenninger's story is interesting.  In the 1940s went to the Bahamas to teach at a Benedictine school there. He was asked whether he wanted to teach English or math.  He chose math. But not having taken many math courses in college, he struggled at first to stay a few pages ahead of the students!  He taught algebra, Euclidean geometry, trig and analytic geometry. 

In the 1950's he felt he was getting stale, so he went to Columbia Teachers College in the summer for 4 years.  He got interested in the “New Math"... and started studying polyhedra.

In 1966 he wrote a booklet called Polyhedron Models for the Classroom.  He wrote to H. S. M. Coxeter, the world's expert on polyhedra and higher-dimensional polytopes, sometimes called the 'king of geometry'.   Apparently Coxeter sent Wenninger a copy of his book Uniform Polyhedra

A uniform polyhedron is one that has regular polygons as faces and is symmetrical enough that there's a symmetry carrying any vertex to any other.  There are 75 uniform polyhedra - not counting the infinite list of prisms and 'antiprisms'... and a very weird thing called the 'great disnubdirhombidodecahedron'... which is a topic for another day.

After getting Coxeter's book, Magnus Wenninger spent a lot of time making models of uniform polyhedra. He made 65 of them and put them on display in his classroom. Then he decided to publish a book about them. He had the models photographed and wrote the accompanying text, which he sent to Cambridge University Press.

They said they'd be interested in the book only if Wenninger built all 75 of the uniform polyhedra!  And so he did...

It took him 10 years to finish the book, Polyhedron Models, which was published in 1971.   Mathematics is full of stories of amazing persistence, and this is one!  

The key, which not everyone realizes, is that math is immensely fun.   To leave behind this world of woe and lose yourself in a world of beauty and perfection - it's dangerously addictive.

Puzzle: this shape is covered with little pentagons, little hexagons and funny-looking nonconvex shapes.  How many of each are there?

It only takes a tiny bit of persistence to figure this out... at least compared to Wenninger's persistence.

I got my story from here:

https://en.wikipedia.org/wiki/Magnus_Wenninger

and the image from here:

http://taffgoch.deviantart.com/art/Order-in-Chaos-214480976

#geometry
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Another classic prank

via reddit
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NO, we will NOT forget!  And we will keep reminding ALL voters about +John Boehner , +Eric Cantor ,  +Paul Ryan  voting record. 
Internet never forgets!
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Learning how to learn.
 
How can you get better at figuring stuff out?  

Read this interview for some of my tips.  But I left out an obvious but much-overlooked tactic for solving problems: talk to lots of smart people, and ask lots of questions

Especially in math, there's a bad myth of the 'solitary genius' who cracks a hard problem all by himself.  (Yeah, in this myth it's always a 'he'.)  Remember Andrew Wiles, who spent years working in his attic and finally came out with a proof of Fermat's Last Theorem?  Well, actually that's not quite right.  He didn't start from scratch: first he learned all the best techniques from other experts, and chose a strategy developed by some other people.  Then he held a regular seminar with some grad students where he'd explain his work and get feedback.  And then, his first attempt to prove the theorem failed.  It was on the right track, but it had some holes in it!  So what did he do?  He got a grad student to help him out, and they finished the job.

For every 'solitary genius' that does something great without any help, there must be a dozen geniuses who are smart enough to get lots of help... and even more 'solitary failures' who get stuck or simply delude themselves into thinking they are doing great work, lacking corrective feedback from conversations. 

In the interview, I mentioned the importance of talking to lots of smart people when trying to come up with good research problems.  But it's equally important when you're in the midst of solving them.  Yes, you need to sit alone quietly and think.  But that's just part of it.
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So is this anti-gravity wheel a simple magic trick or cool physics?

A man sorta effortlessly lifts a 42-pound weight at the end of a long rod over his head. It seems like it's floating! What is this sorcery? Is this guy a wizard? Actually, it's just good old physics in action. The phenomenon that makes this seemingly magical act possible is called torque-induced precession—also known as gyroscopic precession.

Torque-induced precession is the phenomenon in which the axis of a spinning object (e.g., a part of a gyroscope) "wobbles" when a torque is applied to it, which causes a distribution of force around the acted axis. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the torque are constant, the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, its weight is acting downwards from its centre of mass and the normal force (reaction) of the ground pushing up on it at the point of contact with the support constitute two opposite and equal forces producing a torque.

You can  watch the demonstration by +Veritasium 's  +Derek Muller > Anti-Gravity Wheel?

The phenomenon doesn't make the weight lighter, although it will feel lighter to person lifting it. Still not clear about how it works? Here's the video that explains it all in detail: > Anti-Gravity Wheel Explained

Bonus
Spectacular lecture from the legendary Prof. Walter Lewin:
> Wheel momentum Walter Lewin.wmv

#science #torqueinducedprecession #gyroscopicprecession  
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I built one in my backyard, an 8'x12' little shed, cozy and very nice.
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Intellectual freedom is one of humanity’s greatest gifts—and biggest burdens. Our ability to ask questions, to test ideas, to doubt is what separates us from our fellow animals. But doubt can be as terrifying as it is liberating. And it’s the terror of doubt that fosters the toxic, life-negating cult...
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"[A] remarkably large number of Americans, including the leaders of our country and the movers and shakers of our public opinion, are so inept at the elementary skills of thinking that they can’t tell the difference between mouthing a platitude and having a clue."
John Michael Greer. 
This one is  classic.  Required reading.  This will be on the test.
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LL Pete
 
I might add that the comments section to Greer's blog almost always has a great number of very informed insightful postings.
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Sadly a brilliant article - The #climate change deniers have won  http://ow.ly/uT1lF #environment 
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I haven't aged since 1976. Curious.
Introduction
I was born at a very early age, on a dark and stormy night, at the height of Empire.

Think orders of magnitude and the number four (4). 
- Geologically speaking the earth has about 4 billion years left, then it's toast -- literally. 
- Biologically or evolutionarily speaking, our species might last another 4 million. Might, maybe...who really cares? 
- 400,000 years and homo sapiens will be as homo erectus (?!?) or homo sapiens archaic seem to us now. 
- 40,000 years and homo sapiens will be culturally more like Neanderthals were then. That will be a good thing. 
- In 4000 years our era will seem like the Egyptian Kingdoms do to us now: gate, gate, para gate, para sum gate
- 400 years -- everything is politically, culturally, economically, and environmentally -- drastically, dramatically, different!  USA no mas! 
- 40 years?  Modern industrial civilization is in collapse even as we speak and has 40 years left in the tank, max. Then Mad Max! 
- Politically, for the United States the next 4 years will mark a sea change.  
- Me, I figure I got 44 years, 4 months, 4 days, 4 hours, 4 minutes and 4 seconds left, give or take.
- I will live to see the first and most dramatic stages of collapse. You should be so lucky. 

In the meantime, "Never clean; after four years it doesn't get any dirtier.  Just don't lose your nerve."

Maxim #!:
Nature bats last.

Maxim #2:  
Tribal identity and belonging is the highest human value.  Everything else is an epiphenomenon -- posturing, posing, and window dressing.

Maxim #3:  
There is no supernatural, anything.  Never has been; never will be.  Ever.  The natural world is everything that ever was, is, or will be.  It is enough and far more than enough.

Maxim #4:
The supernatural is an uncontrollable variable.



Dixi.

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