Renaissance Wrestling

Via the Giant’s Shoulders #16, I found Arcsecond: The Renaissance Man Uniform Gravitational Acceleration SMACKDOWN

The post is interestig enough, but what really got me was the following pictoral representation of perfect squares:

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If you keep adding up the odd numbers, you get the next perfect square (i.e. sum the quantity (2i-1, from 1 to k, and you get k^2). You see this by adding a new “L” of dots to the previous square, which always has 2 more dots that the previous one, i.e. it’s the next odd number in the sequence, and it makes a new square.

That is so cool! If I had previously known this, I had forgotten it. And I can easily imagine this being taught to me ages ago, and not making quite the same impression because I couldn’t fully appreciate the elegance of it.

Saturn at Equinox

The Big Picture: Saturn at equinox

Checking in with NASA’s Cassini spacecraft, our current emissary to Saturn, some 1.5 billion kilometers (932 million miles) distant from Earth, we find it recently gathering images of the Saturnian system at equinox. During the equinox, the sunlight casts long shadows across Saturn’s rings, highlighting previously known phenomena and revealing a few never-before seen images. Cassini continues to orbit Saturn, part of its extended Equinox Mission, funded through through September 2010. A proposal for a further extension is under consideration, one that would keep Cassini in orbit until 2017, ending with a spectacular series of orbits inside the rings followed by a suicide plunge into Saturn on Sept. 15, 2017

The Rose-Colored Glasses of Success

Missed Kicks Make Brain See Smaller Goal Post

The researchers used a small, adjustable replica of a goal post to test players’ perception before and after attempting 10 kicks. While standing in front of the real-life goal, participants were asked to adjust the width and height of the model to scale.

The players’ pre-performance estimations didn’t correlate at all with their subsequent success rate. But after 10 field goal attempts, their perceived goal size was highly correlated with peformance.

Interestingly, the change in players’ perception didn’t just depend on how many goals they missed — it also mattered how they missed their goals. Folks who failed because they didn’t kick high enough perceived the crossbar to be taller, while those who kicked to the side viewed it as more narrow.