Monday, January 27, 2014

The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we concluded we could take arbitrary steps perpendicularly off-diagonal

(x - n) (x +n) = x^2 - n^2

Look ma, algebra without algebra!

It's moments like these that make it hard to remember that we need to praise hard work over Smartness. But it's true. Owen thinks about numbers deeply and frequently. Practice leads to creativity, creativity leads to intelligence as his genes encode experience. The boy's brain is growing without bound!

Latex in Blogger

Let's see here...

\int x dx = \frac{1}{2} x^2 + C

Sweet! Blogger understands more LaTeX than I gave it credit for. The line above is created with:

Here are instructions on how to set up Blogger to do this (just drop snippet of code into the Template's HTML code after the <head> line).

Tuesday, January 21, 2014

Wha?! 1+2+3...+N = -1/12

Update: People who know math deeply (i.e. not me) hate this video. Those people have spoken, loudly. Thx math people! Side note: Summing the number of planets in the Galaxy will never yield -1/12, so my research is safe...

Via Phil Plait on, a little bit of mathematical hokus pokus:

Sunday, January 19, 2014

The need to recognize that good people can do bad things

I recently had a discussion with some fellow astronomers at an off-campus function about diversity and best practices in hiring for academic jobs. I was advocating taking active measures to ensure that unconscious biases were avoided or at least marginalized. However, as discussions of personal biases tend to go, one of the participants in the conversation took offense at the notion that he might be biased. This is understandable since no one wants to count biases among their defining characteristics.

I attempted to assuage his concerns by telling him that one can have biases and act in a biased manner without being a biased person. I feel this distinction is important. It goes for racist and sexist behavior, too. I can act in a sexist manner, perhaps (often?) not even trying to, without being a sexist person (and to be sure, I have done so in my past ). Similarly, someone I work with and admire greatly can say something that is racist and I can take offense to their statement on the grounds that the statement was racist. But by taking offense and calling out the action, I am not saying that my colleague is a racist person. They were not born a racist, doomed to forever walk the earth with a white hood over their head. But even the best of us well-intentioned, decent people can occasionally slip up and say something offensive.

Saturday, January 18, 2014

Junior Aerospace Engineer: NASA's F-15B

Did you know that NASA has a fleet of F-15 Eagles? Well, they do and they use them in the name of Science rather than war (NASA page). Marcus and I found out about these special F-15's through one of his fighter plane books from the library. Of course, Marcus had to make one of his own (with help from Dad and Mom). I did the difficult folds as prescribed by one of Marcus' paper airplane books (again, from the public library) and Erin built the red test device that is affixed to the plane's fuselage:
Eagle Aero probes fly attached to the red device underneath NASA's F-15B research test bed aircraft during a test flight in early 2011. (NASA / Carla Thomas)
Marcus' model of the NASA F-15B research test bed, complete with red test device
Check out all of those precise folds by yours truly. Marcus modified the
design by adding a cock pit (curved piece of paper on top where the pilot sits)

Thursday, January 2, 2014

The benefits of being a mentor in academia

Yoda gets a nice benefit from his mentee.
Today's guest post is by Wen-fai Fong, a graduate student in the Harvard Astronomy Department. Wen-fai will be graduating with her PhD this coming Spring and she studies the galactic environments of gamma ray bursts (GRBs). Since arriving at Harvard, I have been very impressed with Wen-fai's leadership and initiative in establishing mentoring within the astronomy department. Her efforts include the establishment of a peer mentoring program similar to the program I benefitted from at Berkeley, and a new faculty-peer mentoring program. The programs were recently recognized and funded by Harvard University through a GSC grant. Given her experience over the years with mentoring, both as a mentor and mentee, I asked her to share her thoughts on this blog.

Lying on my couch on Thanksgiving Eve, nearly comatose from uncomfortable amounts of turkey sitting in my stomach, I flipped on the TV. To my delight, Star Wars: Return of the Jedi was playing. A few commercial breaks later and I was wide awake, weeping during the scene in which Yoda dies. This got me thinking: Yoda was such a fantastic mentor to Luke Skywalker, and Luke obviously went on to do great things. But what the heck did Yoda get out of it? I let these thoughts dangle in my mind as I dabbed my eyes, changed the channel and told myself to get a grip!

Many articles I’ve read concentrate on the benefits of being mentored. Indeed, these studies have contributed to the ubiquity of mentoring programs in working environments. From business schools to medical schools1, from small start-ups to tech moguls like Google... even the U.S. military2 recognizes the impact of mentoring on the mentees. But why should people want to be mentors, especially in the stereotypically emotionless world of science and academia?