### On the number of guns and planets out there, Part 1

Ta-Nehisi Coates recently asked his readership to "talk to him like he's stupid" about gun ownership rates in the US and in other countries. I really like it when he makes these requests. It's how I often feel about stories in the news, which make me feel like I'm walking in on the middle of a grown-up conversation. I need someone to talk to me like I'm stupid about Benghazi or the fiscal cliff. Fortunately, Slate and Salon are good sources for this sort of information, as is Andrew Sullivan.

Anyway, regarding gun ownership rates, the discussion that Ta-Nehisi sparked got a bit muddled over the question of guns per capita (number of guns per person) versus the number of guns per gun-owner. This is an important distinction. There are two ways to get 1 gun per person in a hypothetical town of 100 people. One way is to give a gun to every person in town. The other is to have one person in town with 100 guns.

Of course this whole discussion goes back to the most recent mass shooting. But when I read it, my mind drifted into a much nerdier direction, as it is wont to do. Call it a coping mechanism. Or just call me a nerd.

What I immediately thought about was the question of the number of planets in the Galaxy, which Jon Swift, myself and our collaborators touch on in a soon-to-be posted paper about planets around red dwarf stars in the Galaxy. Long story short, we come to the conclusion that there is one planet per star throughout the Galaxy. Given that the Galaxy has 200 billion stars, and that 70-80% of those stars are red dwarfs, that's a whole lot of planets! Of order 100 billion planets in our Galaxy...as an order-of-magnitude estimate...of the lower limit.

This many: 100,000,000,000+

But the way in which those planets are distributed throughout the Galaxy matters. Is that literally one planet per star, or no planets for most stars with dozens of planets around a few stars? The number we quote in our paper and in our upcoming press release makes for good press: billions and billions of planets! It's also good fodder for Drake Equation discussions (for what those conversations are worth). But from the standpoint of planet-hunting, we're more interested in the fraction of stars with at least one planet (think of it as the fraction of stars with planetary systems), and the number of planets per system.

In analogy to the gun discussion, it's the number of guns per capita, versus the number of gun-owners, versus the number of guns per gun-owner. The correct statistics depends on what question you want to answer. I'll get to the math of the matter in my next post.

### 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…