Notes from Maine - 2025/02/02

We’re having a nice, cold February morning and I’m thinking about math. Quick disclaimer—I have no real ability to learn or teach math. I’m pretty good at math, but I’m just terrible at learning it. Everything I know is stuff that just made sense to me along the way. The teacher at the front of the classroom had very little to do with it. Because I didn’t understand the steps on the path to understanding, I really can’t effectively explain anything. All that said, I’ll do my best.

In linear algebra, there are things called “vectors.” If you had a sheet of paper, and you drew a little arrow on the paper, you could call that arrow a vector. It has a size and a direction that it goes. If you had two vectors, you might wonder what those two vectors have in common.

This is where I’m struggling with an analogy. I don’t want to just parrot what some website says about the subject, so I’m going to relate this back to kitchen remodeling. I’ve been doing a lot of that lately too.

Over the years, I’ve built a bunch of drawers for furniture. The drawer boxes turn out okay, but once I install them they just don’t seem right. My sister used to do woodworking. One time we collaborated on a piece for my father. It was a TV stand with shelves and drawers underneath for his remote controls, manuals, and then all the devices. It held a DVD player, cable box, amplifier for his speakers, and a whole stack of DVDs that nobody could ever remember watching. My sister built the drawers in Virginia and then we mounted them when she brought them up. They were perfect drawers, and there was nothing wrong with the cabinet that we installed them into, but they were never quite right. The gaps around the edges were just slightly off and one opened more fluidly than the other. Dad never complained.

I think the problem was the drawer slides. They were side-mounted and it was difficult to get the spacing and all the angles perfect. Shouldn’t have been hard, but it was. For my kitchen, I did a bunch of research to find the perfect drawer slides. I settled on Blum tandem drawer slides. They mount under the drawer box, so you lose a little height, but they are wonderful. They slide in and out with almost no friction or chatter, and they allow no vertical motion at all. 

Back to vectors—imagine the arrow we drew above, but the arrow represents a force that we’re applying to a drawer. If that force is trying to pull the drawer out or push the drawer in, it’s 100% effective because the slides are made for that type of motion. But if you try to press down on the drawer or lift it up, the drawer doesn’t move because the slides are strong and built to hold a lot of weight.

I mentioned that I was struggling to come up with an analogy. Do you believe me now? 

Imagine a new vector that’s not completely trying to push a drawer in, and it’s not completely trying to lift the drawer, but it’s a diagonal vector (equal parts up and in). Some fraction of the force is trying to lift the drawer and some fraction is trying to push it in. The drawer can’t move up, but it can be closed. So only a fraction of the force will take action on the drawer. We can calculate the amount of force that will be effective by taking the “dot product” of the force against the motion that the drawer allows. 

This analogy is tortured and I fear it’s failing to get my point across.

I was thinking about vectors and dot products because I was thinking of the things we say to each other during the course of normal conversations. Someone trying to hurt my feelings might say to me, “Wow, you look dumb with those thirteen fingers flying all over the place. You trying to play two pianos at once with those thirteen fingers?”

I wouldn’t take offense at all to that jibe. I don’t have thirteen fingers. The “dot product” of their insult to my reality has zero result. The resulting force acting on my feelings is nothing at all. However, if they said something like, “Your face is so puffy it looks like a catchers mitt left out in the rain. Your eyes have more bags than a one-way flight to Fairbanks.” That comment might hit home a little. I’m getting old. My skin hangs off my skull in weird ways. It only really occurs to me when I pass by a mirror. Easy fix—fewer mirrors. But if someone said that to me, the dot product of that quip versus my own self-image would have force.

I try to keep that idea of a “dot product” in mind whenever a comment bothers me. I’m a reasonably secure person. I can let unfounded observations roll off my back. But if something resonates and sticks with me, it’s likely because it’s something that has already crossed my mind. On a TV show once, a character said, “If you’re waiting for the cashier to look before you put your tip in the jar, you’re tipping for the wrong reason.” Is that true? Is it wrong to want the staff to know that you’re one of the good ones? If we’re tipping to reward good service, they have to know who left what so they know which service was notable, right? Or am I just obsessed with being thought of as a good person?

I’m drowning in bad analogies and anecdotes at this point.

Back to the kitchen—we finally got the Range Hood mounted last night. It took several tries. I still have to run the ducting, but at least it’s installed. Last night, I was plagued by dreams of air flowing in the gaps behind my cabinets. I don’t know why that idea bothered me, but it did. Maybe once I cut the hole in the side of the house I will feel more settled. For as long as I’ve “owned” this house and probably for as long as it has stood, it has had a “Wish Hood” instead of a “Range Hood.” A “Wish Hood” is where you burn food on the stovetop and Wish you had a way to vent the smoke to the outside because nobody ever installed a Range Hood. I’m very close to finally solving that problem.