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4!-torsor a la George Hart

20 April 2015

As a project with a certain 4-year-old relative of mine, we constructed the proof I described before that the outer vertices of George Hart’s 12-Card Star form a 4!-torsor.  (I guess I didn’t say it that way before, but it’s true!)  Here’s our proof:

IMG_2215Last time I suggested using a deck of 12 cards like this:

deckoftwosBut instead, we used four solid colors, three cards of each.  So, our “star” permutes the colors red, white, black, and silver:

IMG_2090

You can get any permutation of these colors in our Star by exactly one symmetry taking outer vertices to outer vertices.  The “exactly one” in this isomorphism is what makes the set of outer vertices a 4!-torsor rather than just a 4!-set.

Here’s what it looks like when you put three pieces together, from both sides:

IMG_2210IMG_2212

Observer Space: new paper and ILQGS talk

3 October 2012

Steffen Gielen and I just put our new paper on “observer space” on the arxiv:

S. Gielen and D. Wise, Lifting General Relativity to Observer Space

Then, today I gave the International Loop Quantum Gravity Seminar on the same topic. This a seminar between various institutions, mainly in North America and Europe, where people work on loop quantum gravity and related topics. It’s run the old-fashioned way, as a conference call.

I was a bit uneasy about volunteering for such a talk. I don’t like phones. I’m happy to speak in front of any audience I can see — but an audience I can’t see is a little intimidating, even if I do probably know most of them. Besides, on the phone, you never know whether someone might be recording your conversation, hoping to use it against you later. And in this case, they were! Here’s the audio to my talk in aiff or wav format. If you decide to listen to that, you might also want to look at the slides to my talk.

Seriously, I think the talk turned out rather well — except for the part where my Skype connection to the phone bridge cut out, and I didn’t even know it. Fortunately, though, as I only found out after the talk, Steffen took over, explaining to the audience the same stuff that I was simultaneously, unwittingly, explaining into a black hole. Steffen had never seen the slides, and described this as his first experience with live Powerpoint karaoke. I think he did an excellent job of filling in.

I’ll have to explain a bit more about “observer space” on this blog sometime later…