### And We Settled for Mediocrity

This, y'all:
This got me thinking again about a revelation I had not long ago, but admittedly not long enough ago. I'm going to explore some tough truths here. So before I get going, let me explicitly state some of my working assumptions. First, I believe that all humans, no matter how one cares to group them, whether by race, religion, physical ability, gender, sexuality, possess the same distribution of intellectual abilities. For example, I believe that a group of 100 undocumented, Lutheran, Latinx transwomen have the same distribution of mental talents as a group of 100 straight, cisgender, white, atheist men. Can I prove this beyond doubt and within 0.1% precision? Nope, probably not. But it's an historical fact that the biological and social sciences in Europe and US America have focused on this question for most of their existence, with the explicit aim of proving the superiority of the latter group. Given that these fields have thus far failed to find evidence to support the superiority of one group over the other, I feel fairly confident in this assumption.

Anyone disagree with this assumption? If so, please read no further, because A) you won't find much that you like in what follows and B) "This...person I am not trying to convince".

My assumption of equality naturally leads to the conclusion that the lack of any specific group from academia or any other intellectual pursuit is not a natural outcome, but instead due to actions that keep them out, not because they can't do what is necessary to be there. Our society tends to focus on words that describe the state of being at the exclusion of the actions that lead to that state. This is why we focus on diversity, and the lack thereof, while going out of our way to avoid naming the features of our societal landscape, and the actions of people who traverse that landscape, that exclude specific groups of humans and leads to a reduction of diversity that would otherwise be present. Since groupings of people are meaningless when selecting for things like intellectual acumen, creativity and general talent, a paucity of diversity is an unnatural outcome that must be the result of factors extrinsic to the missing groups.

I hope that I have lost many of my readers thus far. Okay, now for the hard truths.

Since the lack of diversity in our field is the direct result of exclusion, our culture of exclusion has resulted in a cohort of scientists that is less talented than what could have been. To be clear, I am not detracting from the accomplishments of those who currently work in the field. Having been admitted into the pursuit of knowledge through scientific inquiry, it was undoubtedly necessary to invest hard work and dedicated practice in order to do the things that scientists have thus far accomplished. In absolute terms, the discovery of, say, the accelerating Universe or putting telescopes into space are amazing triumphs of human inquiry and ingenuity. But in relative terms, they aren't even close to where we would be if we drew talent from the full pool.

This isn't a multiculturalism-based platitude; this flows naturally and directly from my starting assumption that all people are created equal. Indeed, it pushes back to the sentiment too often found in multiculturalism efforts: that the simple presence of non-white people and their special ways of doing things improves things for white people. Forget that mess! The people you don't see around your institution? Those people are smart human beings who would help our field achieve its (stated) goal of learning more about the Universe.
 Astronomy's unbearable whiteness of being was, and is, created.
It is a simple fact that in 1960, white men, and just about only white men comprised the applicant pool for astrophysics graduate programs in the US. It is well documented, if not always remembered, that this was due to the explicit and deliberate exclusion of everyone else. If you haven't read Risa Wechsler's excellent article about the late Vera Rubin, you should soon. One part that stood out to me highlighted the processes of exclusion that people like Vera faced when trying to find a way into astronomy:
Vera faced isolation and exclusion at many turns. Her high school physics teacher told her: “As long as you stay away from science, you should do okay.” Princeton wouldn’t even send her a graduate school brochure because they didn’t admit women at the time. She once had to have a meeting with a famous astronomer in the lobby of his building because women were not allowed upstairs in the offices. In the mid 1960s, she was the first woman allowed to use the telescope at Palomar Observatories, where she later did her most groundbreaking work.
This is what active exclusion looks like, and Vera's experiences weren't unique or even aberrant. It was accepted and often official policy, and it directly aided white men by reducing their competition.

At that time, white men made up 42% of the US population, which meant that a 23-year-old white man applying to graduate school was competing against roughly 40% of the pool that would be available without race-, gender- and sexuality-based exclusion working in his favor. The result is that he had a 2.5 higher chance of admission based on the number of applicants alone. If I were to tell you that the next time you apply for a job (or fellowship, or grant), that I could boost your chances by a factor of 2.5, I think you'd be pleased at that prospect. That is, if I didn't tell you it was because I rigged it such that 60% of the other applications/proposals were not even reviewed.

Again, the people (men) who were hired in 1960 and who are still working in the field today have certainly put in a great deal of work and accomplished amazing things. Indeed, the most successful of them would have been admitted and matriculated from a fuller applicant pool. There is no doubt about this. But as it was, the starting conditions were also rigged in their favor. This means there were more talented women and men around at the time who could have become senior astrophysicists today, but are not around because our society arbitrarily weeded them out before they could put in their hard work and achieve greatness in our field of science.

This isn't necessarily a polite observation, and it certainly won't flatter many of my white male peers. But when we look around us and see 90% of the field of astrophysics is white, and that the senior members are predominantly white men, we are not seeing a natural nor optimal outcome. It works well for what it is, but this is like saying that a sprinter had a great finish despite wearing ankle weights. The senior Latinx transwomen missing from our leadership are absent not because they lack the potential for excellence and are less talented as their white male peers. They aren't here because people in 1960 convinced themselves that Latinx transwomen were not only inferior intellectually, but that their place within our society was far from the halls of academia. And they didn't do this arbitrarily. They did it, and still do it to actively affirm the place of white men in our society.

So you know what? Forget discussions about diversity. Let's first talk about what we've lost by settling for mediocrity when we could have had excellence on an absolute scale. Let's explore why we made that decision and how we continue to do so today as we create our culture. Because without this actions-based discussion we're just going to get confused, frustrated and eventually apathetic about our current state. Or worse: we might just accept our demographics as a natural outcome because, you know, people simply aren't created equal.

### 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…

### The Long Con

Hiding in Plain Sight

ESPN has a series of sports documentaries called 30 For 30. One of my favorites is called Broke which is about how professional athletes often make tens of millions of dollars in their careers yet retire with nothing. One of the major "leaks" turns out to be con artists, who lure athletes into elaborate real estate schemes or business ventures. This naturally raises the question: In a tightly-knit social structure that is a sports team, how can con artists operate so effectively and extensively? The answer is quite simple: very few people taken in by con artists ever tell anyone what happened. Thus, con artists can operate out in the open with little fear of consequences because they are shielded by the collective silence of their victims.
I can empathize with this. I've lost money in two different con schemes. One was when I was in college, and I received a phone call that I had won an all-expenses-paid trip to the Bahamas. All I needed to do was p…

### 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…