Hexaflexagons

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Wikipedia

The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone, who was studying at Princeton University in the U.S.A. in 1939. His new paper in America wouldn’t fit in his English binder so he cut off the ends of the paper and began folding them into different shapes.[3] One of these formed a trihexaflexagon. Stone’s colleagues Bryant Tuckerman, Richard Feynman, and John Tukey became interested in the idea and formed the Princeton Flexagon Committee. Tuckerman worked out a topological method, called the Tuckerman traverse, for revealing all the faces of a flexagon.[4]

Flexagons were introduced to the general public by the recreational mathematician Martin Gardner, writing in 1956 in his first column of “Mathematical Games” for the Scientific American magazine.[5] In 1974, the magician Doug Henning included a construct-your-own hexaflexagon with the original cast recording of his Broadway show The Magic Show.

1976 Rhodes Suitcase 88 Key

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Last weekend I jumped at a Rhodes 88 key listed on Craigslist. Looking past the rough tolex and one missing tine/tonebar, this thing is amazing. The boys and I have already put in a few hours of “Frosty the Snowman” and Christmas tunes; I’m looking forward to the many hours yet to come.

Here’s a short tune from Eli (the eldest) and I, Nighttime Rhodes

The 40-Year Slump

What has vanished over the past 40 years isn’t just Americans’ rising incomes. It’s their sense of control over their lives. The young college graduates working in jobs requiring no more than a high-school degree, the middle-aged unemployed who have permanently opted out of a labor market that has no place for them, the 45- to 60-year-olds who say they will have to delay their retirement because they have insufficient savings—all these and more are leading lives that have diverged from the aspirations that Americans until recently believed they could fulfill. This May, a Pew poll asked respondents if they thought that today’s children would be better or worse off than their parents. Sixty-two percent said worse off, while 33 percent said better. Studies that document the decline of intergenerational mobility suggest that this newfound pessimism is well grounded.

via The 40-Year Slump.

Children’s language development: Talk and listen to them from birth.

Six years ago, Suskind noticed a disturbing trend among her patients at the University of Chicago Medicine: While children from affluent families were starting to speak after implant surgery, those from low-income families lagged behind.Why? The question ate at Suskind, who co-founded the hospital’s cochlear implant unit in 2006. She believes she discovered her answer in research by child psychologists Betty Hart and Todd R. Risley. Their landmark study in the 1990s found that a child born into poverty hears 30 million fewer words by age 3 than a child born to well-off parents, creating a gap in literacy preparation that has implications for a lifetime.

via Children’s language development: Talk and listen to them from birth..

Against Redshirting: Why It Pays to Be the Youngest Kid in Class : The New Yorker

Our three year old is in school simply because he’s ready to be there (wants to learn), but worry that as the years go by he might be at a disadvantage by being younger than his peers.  This is interesting and timely:

The less mature students, on the other hand, experienced positive effects from being in a relatively more mature environment: in striving to catch up with their peers, they ended up surpassing them.

via Against Redshirting: Why It Pays to Be the Youngest Kid in Class : The New Yorker.