### Saturday Morning Mathematics

Saturday morning Owen and I were having some fun with math (Marcus helped by turning an otherwise orderly counting process into more of a Monte Carlo process). We started by counting the change in his piggy bank: 1363 pennies in various denominations. While putting the change back in the bank, Owen paused and said, "Daddy, do you know what 37 plus 16 is? It's 53!" I figured he got pretty lucky since we normally do double-digit addition on paper, not in his head. Assuming it was just a fluke, I asked him what 55 plus 13 was. He paused, and I thought he was stumped. Then, after about 10 seconds he exclaimed, "Oh, I know! It's 68!" Well, I'll be!

So I grabbed the camera as we proceeded down the stairs:

I'm pretty amazed at his ability to compute in his head. I think he has a real talent for visualizing numbers and manipulating them spatially (if that's the right term). My mom often recounts the story of me, when I was 5, telling her how many quarters were in two dollars, then three and four dollars. But Owen also has an amazing memory, which is something I lack. I often joke that I have a good processor and fast RAM, but a faulty hard drive (I'm doubly hamstrung because I don't do a good job of keeping notes). Owen's hard drive is like a vault.

Sorry to boast on my boy, but I'm definitely one proud father. As long as he's interested in playing math games, I'm more than happy to oblige. Of course, he may grow up and want to enroll in theater school. If he does, I'll support him fully. But for now, I'm gonna enjoy all the math and football.

jcom said…
Wow what a smart kid! Lemme know if he's looking for a summer REU.
blissful_e said…
Awesome!! Go Owen!!

### 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 started by downloading a stock photo of J.J. from NBA.com, which I then loaded into OpenOffice Draw:

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…