Lawn Theory 101

Four years in this house and I have yet to find a Hamiltonian circuit of the lawn. Curse you NP-completeness!

Explanation: In graph theory, a Hamiltonian circuit is a path that starts at a point in a graph, travels through all other points in the graph exactly once, and returns to the starting point. Determining whether such a path exists in a graph is an example of what's called an NP-complete problem, which means (among other things) that there is no known algorithm of polynomial time complexity for solving it. In other words, it's really hard.

Consider my lawn to be a collection of points, with each point connected to the points closest to it by an edge. Now it's no longer a lawn, it's a planar graph! Thus, we can apply graph theory, and the most efficient way to mow my lawn is the Hamiltonian circuit that starts (and ends) closest to my garage.

You know, for $30 a mow, you can just pay the local lawn guy to do it while you play computer games.

I really should be thinking of it as a Travelling Salesman Problem instead. In that case, I attach a weight to each of the edges in the graph (the length of the edge) and then solve for the shortest tour of the vertices. It's still an NP-complete problem, but now I not only mow each part of the lawn only once, I also travel a minimal distance in doing so. I can't solve it, but if I could it would give me a better answer.

You think about this stuff while vacuuming, too, don't you?

Yes. And mopping the floor. Mopping the floor is easier to visualize because the floor is neatly broken down in to tiles. It's more difficult, however, because you have to take into consideration that you can never stand in a place where you've already mopped.

This is why mathematicians never work as landscapers or housecleaners.

Interestingly, those jobs are often taken by immigrants who speak little or no English, and therefore have better communication skills than most math majors.

It kind of sucks the fun out of things when you make fun of yourself.

It sure does!

Can we talk about toasters now?

No.

Sunlight + Rain^2 = Growth

Our lawn is the only thing around here growing faster than my daughter.

Explanation: I thought my daughter was growing quickly. In less than two months, her bodyweight increased by 50%. That's pretty impressive in my book. She, however, has nothing on my lawn.

My yard (the back in particular) tends to be wet.* My normal rule of thumb is that I need two dry days in a row before I even bother trying to mow. Unfortunately, this time of year does not afford me two dry days in a row EVER. Just ask my poor grill, which hasn't been dry enough to cover for the past week. I'm thinking about going out there with a blow dryer. But I digress.

The lawn is now taller than any respectable homeowner's lawn should ever be, and yet it is still too wet out there to mow. Even worse is that the dandelions out there are growing twice as fast as the grass. In one week, since I last mowed, I have had a few dandelions grow to about a foot tall. At that rate, I think you could actually sit outside and see them growing. Give them some acne and a voice that cracks all the time and it would be just like looking back in time at myself in high school.

*Ironically, my daughter (the back in particular) also tends to be wet.

Time is Money

Were those five minutes of my time really worth the 20 cents?

Explanation: Last night I got a text message. It wasn't from someone I knew - it was some MP3 service sending me spam of some sort. I've never seen a text like that before. The details don't really matter. The important fact is that I have text messaging blocked on my phone... or at least I thought I did.

This is the kind of thing that really drives me nuts. I'm supposed to have text messages blocked. I clearly don't anymore. There's no way I'm going to let Verizon charge me 20 cents for a text message that I shouldn't have received in the first place. No way. Plus, this message might be the tip of the iceberg. I had to nip it in the bud, so I gave Verizon a call.

After five minutes on the phone with Verizon, we established that my block had been removed for some reason. The block has now been re-applied to my account. They were unsure if the 20 cents would be refunded to me automatically, so I have to check my next bill and let them know if the charge is still there (more time and effort) to make sure I'm not paying for a text message I didn't want in the first place.

From a sheer economic standpoint, this drives me insane. My time is money. Now, how much money one's time is worth is a different debate, but I like to base decisions on an amount that I think I could easily earn in an hour's time. The New Jersey minimum wage is currently $7.15, so that's a safe place to start. I like to think I bring a bit more to the table, so I generally assume $10 an hour. Certainly I could make more than that if I was working harder, but I feel like that's a wage I could pull in without really exerting myself too much.

Once you have a dollar value, decisions are easier. Do I pay the neighborhood guy $30 each time he mows my lawn? Well, I can mow my entire lawn in about an hour, so I can consider that as $10 worth of time. Is it worth paying $30 to preserve $10 worth of time? No way. I'll mow my own lawn.

Now, obviously some experiences have some intrinsic value (or lack thereof) that you have to include as well. Would I spend $30 for the neighborhood guy to spend an hour removing the poison ivy from my backyard? Sure I would. My time is worth $10, and not spending an hour handling poison ivy is worth much more than $20 to me.*

On the other side of the coin, I wouldn't pay the guy $5 to wash my car for an hour on a hot summer afternoon. Sure, my time is worth $10, but spending an hour in the cold mist of the hose is worth way more than the $5 I'd save by letting him do it.

Now, let's consider my phone call. I spent 5 minutes of my time in an effort to save 20 cents. That's an hourly savings of $2.40. My time is worth about $10 an hour. You do the math. Even worse is the fact that A) you just know they're going to screw up my bill anyway, so I have to keep an eye on it and B) when they do screw it up I'm going to have to spend ANOTHER 5 minutes on the phone with them. That takes me up to about 15 minutes of total effort, taking the hourly savings down to 80 cents an hour.

So, in short, I hate Verizon. And now I have the math to prove it!

*Plus, I have to add value for the pleasure of knowing that guy is going to be itching for the next two weeks. That'll teach him to up his rates!

The Fun of a Fall Mow

Enjoying my pretty lawn while it lasts.

Explanation: After about three weeks of not mowing, I finally got the mower outside and did the lawn last night. Now that the sprinkler issue has been resolved, the ground was pretty dry, so that helped, but I had a lot of growth in the backyard and a lot of leaves in the front yard.

I'm sure I've complained about this before (and I'm sure you homeowners already know this) but there are two things I particularly hate about mowing the lawn this time of year.

First is the amount of volume the leaves add to the mower bag. On a normal summer mow, I empty a full bag twice and then empty the bag again when I'm done just so it doesn't stink up my garage. Yesterday I emptied the bag at least ten times. It was ridiculous. Mow down, mow back, mow down, mow back, empty the bag. And repeat. Sometimes I couldn't even get four trips in. The mulch pile behind my house went from being 2 feet high to being 5 feet high. I'm glad the grass isn't growing as fast these days, because I'd hate to do this more than once every other week.

My second issue is the more upsetting part - there are still leaves on the trees. Last year I mowed the front lawn and all of the leaves were gone and it looked so pretty... until the next morning when you couldn't tell that it had been mowed at all. This year fall isn't that far along, but the trees out there are just mocking me. I know my pretty lawn isn't going to last. It cheapens the whole mowing experience.

Anyway, my lawn is pretty right now and will remain so for at least fifteen more minutes, so enjoy it while it lasts!