### Intelligence in Astronomy: What Is Intelligence? (Part 2)

One night in Cambridge, England in the late 1970's, two astrophysics postdocs were sitting at a table outside of the Ft. Saint George Pub. One of the astrophysicists was Ed Turner (Princeton) and the other was Scott Tremaine (Institute for Advanced Study). As my good friend, Ed Turner, tells the story
At some point we fell to debating which of our famous senior colleagues was the best scientist.  Ostriker, Rees, Peebles, Lynden-Bell and others appeared in the conversation. We failed to find a compelling case for any one of them or even for comparing any two of them; generally there were arguments for many or both alternatives re who was the best.  I can't recall whether we discussed only theorists or also some observers.
Anyway, at some point we noticed that while it was very hard to say whether X was better than Y or vice versa as an overall scientist, it was often relatively easy to say which was better at some particular aspect of science...like who had the most extensive and detailed knowledge or who was more creative or who picked the best problems etc.  I recall making some analogy to comparing baseball players; it is hard to say who is the best overall but relatively easy to say who has the highest batting average, hits the most HRs, steals the most bases etc...
From this point it was only a short hop into science nerdery as they imagined the various components of excellence and traits of successful astronomers as basis vectors in a multidimensional hyperspace, which they termed the 7-Dimensional Scientist Hyperspace (7DSH, pronounced "seven-dish," I guess :). The seven dimensions of excellence that they identified was some version of the following according to an email Scott Tremaine sent me in response to my inquiry:

Taste  - Ability to identify an important question that can be addressed with the skills that you possess.
Intelligence -   Adeptness at the basic problem solving, calculating, perceptual skills needed to work the problem.
Grit - Ability to do the hard extended work needed.  Ability to maintain attention.  Ability to complete. The ability to face struggles and push through.
Knowledge - Breadth and extent of the corpus of knowledge needed to solve the problem and bring in interesting external information.
Curiosity - Alertness to interesting paths, byways, anomalies, etc.
Luck - Intuitive ability to expose oneself to, select for, and respond to constructive paths.

I really like these dimensions. Note, however, that they do not necessarily form an orthogonal basis set. One cannot be lucky or creative or curious without gaining the necessary knowledge. One cannot communicate well without good taste in selecting the right questions.

Note also that these traits are not static qualities of an individual, and smartness is only one component of success (mostly closely aligned with a combination of knowledge and intelligence). Even if you don't think you are getting smarter in time, and many people doubt that they are, one's knowledge increases monotonically throughout their lives, curiosity comes through effective communication with others, which generates ideas that can lead to asking important new questions. First-year students don't arrive on campus with this sort of software bundled and pre-installed. These are things that need to be learned, and successful graduate programs focus on training students and helping their projections in these various dimensions grow in time.

 Moving from one-dimensional "smartness" to multi-dimensional excellence
After thinking on 7DSH for a few months now, I've devised my modified 7-dimensional hyperspace of scientific excellence (M7DHSE), which draws upon the Turner & Tremaine conception as well as Sternberg's Successful Intelligence:

Creativity - The ability to successfully deal with new and unusual research problems and situations by drawing on existing knowledge and skills. The ability to connect disparate concepts to devise solutions to outstanding problems.

Curiosity - Alertness to interesting paths, byways, anomalies. The ability to identify important questions that can be addressed with one’s skills.

Basic intelligence - The ability to quickly identify the correct solution to academic, problem-solving tasks by drawing upon fundamental physical concepts.

Knowledge - Breadth and depth of the corpus of information one possesses that can be used to solve problems

Productivity - The ability to understand what needs to be done in a specific setting and then do it at  rate that contributes to the advancement of knowledge throughout one’s field

Communication The ability to advance ideas; generate needed input through positive interactions  with others; and disseminate results in oral and/or written form so that others can use them to advance the field.

Pedagogy - Abilities related to the effective training of the next generation of excellent scientists through teaching, advising and mentoring. The ability to adapt to different backgrounds and learning styles in order to help others learn how to be excellent

How does your ability vector, $\vec{A}$,  project into this hyperspace? What is the magnitude of your vector, $|\vec{A}|$? An most importantly, what is the time derivative of your vector, $d\vec{A}/dt$ and what are you doing to accelerate that growth?

honestjournal said…
A good way to normalize these vectors is to find the unit vectors (see page 5):

https://www.cfa.harvard.edu/~dfabricant/huchra/mapmaker.pdf

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### Finding Blissful Clarity by Tuning Out

It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…

### 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…