Use it or lose it

I should be carefully writing a proof of one of the following statements right now.
The action of a linear transformation T: U → V is completely determined by its action on a basis B = {u 1, u 2, ..., u n} for the domain U. OR
The range of a linear transformation T: U → V is a subspace of the codomain V. OR
The linear transformation T: U → V is one-to-one if, and only if, ker T = {0}.

Decisions, decisions. Which statement shall I prove? Unfortunately for me, my brain is more used to decisions like which of the following recipes shall I make for dinner tonight, or which of the following parks within walking radius should we visit today. My poor brain hasn't done higher level mathematics since, oh, let's see, 1998. These proofs are making me wonder if that part of my brain has atrophied!

Regardless, I must prove what the online Linear Algebra course tells me to prove, for I seem to have NOT lost my procrastination skills that I had perfected in high school. This online course that you have a luxurious year to complete expires in a month and I'm not wasting my $411! Plus, I really do LOVE math and I'm excited to go back to teaching math at some point in the future. At which point I want to have a teaching license.

So my kids have gotten a little less attention and watched a few more videos from the library in the last week, which apparently put our TV over the edge. I think it's fritzed out for good. (So much for my free babysitter!) That's why Xander is begging me to play Cootie with him instead of being mesmerized by the What's in Space? show I so lovingly selected for him.

The Princess and the Helicopter

Xander and Elodie were making some pretty elaborate plans as they sat in the double stroller on the way to the grocery store this morning. We saw two helicopters flying at the same time, which was pretty mesmerizing. Naturally, Xander declared that he wants to fly a helicopter when he grows up. Elodie took this opportunity to repeat her future plans. "When I drow up, I want to be a princess." I was curious about what she thinks that entails. "They dance at the ball," she informed me.

Xander: "Elodie, I can take you to the ball in my helicopter!"
Elodie: "You tan? Tan I dance at the ball?"
Xander: "Yeah. And you can eat dinner on the helicopter. You fold down the seat, and then you put your dinner on it, and then you pull down the thing, and you can watch a movie. Elodie, You. Can. Watch. A movie. While. You. Eat." (He punctuated each word as if that was the most unbelievable thing.)
Elodie: "Oh."
Xander: "And I'll pick you up in my helicopter after the ball. But you can't marry me, because I'm your brother. And you can't marry Dad. No. ... You can marry Cooper. (He's a cute little 3-year-old from nursery.) Do you want to marry Cooper?"
Elodie: "Um, yeah, I do."


Don't you wish you had a helicopter pilot for an older brother? Talk about first class.

Did I hear that right?

I was just chatting with my survivor man who's currently in Middle-of-Nowhere, Alaska. Before we got cut off, I do believe he said that while the beauty and feel of Alaska is everything he'd built Alaska up to be, he wasn't quite as set on moving our family up there due to the cost of living. Was I really on the phone with Aaron? I guess we've become more unified than I realized over these last 6 years! He's putting practical and frugal over wide open spaces and hunting seasons!? And the funniest part is, when he said that his heart isn't quite as set on Alaska as it was, I felt a little let down. I've been gearing up for an Alaskan adventure for years--I think I was starting to get excited. But with that little reality check, our life-after-medical-school suddenly seems so completely up in the air. Although the cell phone reception was pretty shaky. Who knows what he actually said.

Update: Aaron just called from Anchorage, where cell phone reception is quite clear. The first words out of his mouth were, "I really do love Alaska!" He told me he read this post and that his response was, "What have I done?!"

North to Alaska

Today, Elodie woke up from her nap with some exceptional bedhead. She had taken out the darling princess hairdo (thanks to my niece Alyssa for teaching me another way to do her hair!) which resulted in some gravity-defying craziness off to the sides. I told her that she looked like a mad scientist. "No, I'm a happy scientist," she informed me. I realize that this story would be cuter and funnier with a picture, but our camera went North to Alaska. With Aaron, who is so alone up there in the Last Frontier that he has to take pictures of himself. Here he is in front of the Alaskan Native Medical Center where he is doing a clinical rotation in surgery. Yesterday was his first day, so he just observed. But since today was his whopping second day, he actually got to assist in surgery. I kindly (bluntly?) asked him if these surgeons knew that he has no idea what he's doing. Aaron assured me that you're fine if you just follow their instructions to a tee. Wow--he's definitely getting some good experience! The top-notch surgery department and unmatched hands-on experience offered by these Alaskans is definitely a huge plus, but I'm pretty sure that the main reason Aaron is up in Alaska is to convince me that living there will be a dream come true for the whole family. This is the home where he's currently staying. Our bishop hooked us up with some friends of theirs in Anchorage and they've offered him a couch--and food--at no charge. I'll admit, this house could be a dream come true for a large family. I love the wrap-around porch! Aaron is also trying to disprove my notion that Alaska is all glaciers and tundra. You can actually grow a garden up there, believe it or not. Check out the size of their rhubarb!And he claims that these raspberry bushes are taller than he is. Maybe this IS a dream come true! YUM!Every time I talk to Aaron he tells me how gorgeous the views are--mountains jutting straight up from the ocean's edge, with a glacier nestled right in between. Of course cameras aren't very good at capturing spectacular--he assures me that this view is awe-inspiring in person. Which means that all of you will just have to come visit us when we move up North to Alaska so that you can see the views for yourself!

Tiny-Town Texas

We spent the second half of June in a tiny town called Bowie, Texas. That's where Grandma & Grandpa Dahle live these days. While Aaron learned oodles in his rural family practice experience, the kids and I enjoyed the pace of small town life. The biggest adjustment for me was no internet access or cell phone reception--for two weeks! One of my favorite parts was watching Xander bond with Grandpa Dahle. Xander loved to just follow Grandpa around. With all that space, there were plenty of interesting places to follow--to the pond in the corral, to the garden to pick vegetables, even to the driveway to check fluids in the Jeep.

Xander and Grandpa especially loved picking berries together out behind the horses' corral. Unfortunately, Xander liked those berries so much that the bowl always returned to the house as empty as it had been when they left. Grandpa just chuckled, but, hey, I never even got to taste one berry! Grandpa was also Xander's favorite because he knew how to fix the chain that kept breaking on the pedal-powered John Deere. And Grandpa helped Xander make his idea of hauling the wagon behind it a reality. Xander's little cousin (technically, first cousin once removed, but who wants to be technical?) Jaxson was happy to be hauled behind the tractor.And he was equally happy to hop out and help push when the tractor got stuck. They had a blast together!Jaxson and Elodie bonded, too, although Elodie only considered Jaxson and Logan and Braxton and Zach and Cody Xander's cousins, since they are all boys. There were no little girl cousins in Texas, but she was excited to have her "tousin" Tanielle, who's 13, sleep in her bedroom one night. But Elodie really did play well with Xander's cousins, too! Grandma Dahle and Aunt Marj generously threw Xander a Texas birthday party. He came away with numerous new trucks, one of which was a John Deere with various attachments which he informed me today is his best truck. We all had loads of fun with Ryan and Keira's cute little family, even though Ryan and Aaron's hog-hunting plans never quite materialized. (Awwww, shucks!) We really enjoyed the time in tiny town Texas, mostly because we got to really reconnect with people we love most!

Won't my daddy be so proud of me?

I'm cookin' up a pot of garden weeds.

Won't my daddy be so proud o' me?

'Cause I'm cookin' up a pot of amaranth!
Yum! That smells good!

I'm eatin' up a pot of garden weeds.

Won't my daddy be so proud o' me?

'Cause I'm eatin' up a pot of amaranth!

Wow! That's yummy!

Ya know when you come home from vacation and you have no produce in the fridge? Ya know how you come home from vacation and you have GIANT weeds in your garden? Put them together and what do you get? Bippity, boppity, boo! A delicious side of greens! Believe it or not, I heard these exact words out of Xander's mouth when he finished his serving of amaranth" "Yum, may I have some more greens? Those are really good." I think that moment was the highlight of my day! Having greens for dinner really was quite a novelty. Growing up, we generally had them as a midnight snack since my mom (the dinner chef) wasn't nearly the edible weeds enthusiast that my dad (the midnight snack chef) is. If only I'd made a frozen-banana-powdered-milk-honey-milkshake, the experience would have been complete. Mmm, just thinking about it makes my mouth water. It's been too long! I think I'll have to break tradition again and serve it for breakfast this week.

Back Together for the Jamboree

Lowe Reunion Days! Please pass the ketchup! While we were together drinking homemade root beer and gobbling down the homemade ice cream, we wondered why our old family reunion song didn't say "Please pass the root beer." I'm sure Grandpa Lowe had his reasons! With nearly all 100 of the Nola and Julian posterity there, we sure had a blast! Elodie thoroughly enjoyed the chance to play with HER cousins. She calls the boy ones XANDER'S cousins. Elodie even got some chances to dote on "tute baby Haley."Evan and Grant are so good at including Xander as one of the big guys. He idolizes them both! I believe his last words to Evan before we drove off were, "You're awesome!" Personally, I think Jill is rather awesome. I even honored her on the Fourth by making it "Try to be like Jill day."

Unfortunately, I don't think it worked. Her cuteness simply can't be copied. Trust me. I tried.