Real World Subtraction

This page comes from one of Sophie’s summer homework books. It’s just one of many practice exercises in adding and subtracting:

Real World Subtraction

Real World Subtraction

Well, sure! My first thought whenever it’s raining out side is: “I wonder what the difference between the number of puddles here and the number of rain boots might be.”

This sort of infuriating problem is what leads to math being incomprehensible at higher levels. Subtraction isn’t a magical and arbitrary branch of abstract mathematics. It’s a tangible, everyday concept.

Sophie understands that when she spends money and gets change she can calculate the difference with subtraction. It’s an understanding not just of how but why. That’s harder to teach with higher-level mathematics. It shouldn’t be a challenge with elementary arithmetic.


Progressive offers a discount program called Snapshot where they electronically monitor your driving “to get away from the law of large numbers and focus on how you personally drive” (says my agent).

Here’s the deal. First, Progressive monitors three aspects of your driving:

  1. When do you drive? Midnight to 4 am are “high risk” hours. On weekdays, “medium risk” times are 4 am to 9 am, 3 pm to 6 pm, and 9 pm to midnight. On weekends it’s just 4 am to 6 am and 9 pm to midnight. All other times are “low risk”.
  2. How far do you drive? Averaging less than 30 miles per day (over a one week period) is good.
  3. How hard do you brake? Decelerating at 7 mph per second or faster is bad.

That last one is the hardest to intuit, since we don’t have deceleration gauges in our cars. Twice this week I’ve braked suddenly to avoid hazards (e.g., the guy who merged into my lane while I was still in it), and neither registered as a “hard brake”. Two others that didn’t feel sudden to me at the time did register.

Progressive is aware, of course, that sometimes stopping short is the safest maneuver. As my agent put it, “As your insurance company, we’d rather you brake hard than make us buy you a new car.” But doing it too often suggests you’re following too close: you should have time to decelerate gracefully even when the car in front of you stops.

Snapshot Speed Graph

Snapshot Speed Graph

The website shows a detailed graph of your speed during each “trip” (each time the ignition was started and then stopped). Knowing the route, it’s easy to figure out what happened when. Here, I left our neighborhood for the 60 mph highway, stopped at a red light in the middle, decelerated to turn onto a 45 mph road, et cetera. I can even see where I stopped at a light, inched into the intersection when it turned green, and then made my left turn.

But presumably you wouldn’t have deduced my route from my speed alone, and neither can Progressive. The tracking device does not have GPS installed.

(This doesn’t make it any less creepy that I can tell every time my wife stops for a Starbucks from the telltale “mostly stopped with occasional momentary 3 mph spikes” graph and the extra mileage.)

Progressive offers an initial discount after collecting data for 30 days, then a final discount after six to twelve months. “Final” means Progressive offers an initial discount after collecting data for 30 days, and then a final discount after six to twelve months. That final discount is permanent — you keep it as long as you’re insured with Progressive. When they first offered the program bad drivers could suffer a 5% increase, but they phased that out. Now the worst penalty is “no discount” and the best is 30% off.

A couple more facts that may be useful:

  • New trips appear on the website within a few hours.
  • The speed graph is a fixed size, so longer trips just get crammed into the same space, and a lot of the detail is lost. For trips of about five miles, it’s about the right size.
  • The speed graph doesn’t specifically indicate where your “hard brakes” are. You can sometimes tell visually, but it’s guesswork.

On Cruising: The Crew

For our honeymoon we cruised on Carnival Imagination for four days to Cozumel. This is part of a series of anecdotes on the experience.

On our last day aboard, Carnival offered a “Behind the Fun” tour visiting all the crew-only areas of the ship to show how the magic is made. I couldn’t resist! The answer: it’s made through a lot of hard work.

We visited the galley, where a bar of baking chocolate as large as a desk literally and figuratively dwarfed everything else in the room. I ate some of it in the form of cake at the all-you-can-eat chocolate buffet later that day.

We visited the laundry room, where workers fed sheets into giant machines to be folded and ironed, in an endless progression. We tourists got to try our hand at the towel folding machine. As we giggled with goofy delight at seeing an unfolded towel enter, and then drop seconds later into a neatly folded pile, the crewmen’s eyes seemed to say, “You realize we get paid to do this all day, right?”

We visited the bridge, where one officer must always be looking out to sea, while others supervise an array of modern cartographic technology.

We visited the engine control room, where one whole wall schematically depicts the flow of electricity to various ship systems, with an enormous console filled with gauges and buttons and levers stood ready to run the entire ship if needed.

But surprisingly, the visit that’s stuck with me most was the ship’s stores: giant freezers stocked with meat, poultry, and seafood; a refrigerator the size of a large bedroom full of liquor and other beverages; and workrooms to prepare food for the galley. (For whatever reason, chopping vegetables and meats isn’t charged to the galley staff, but to the provisioning department.)

On opposite sides of the ship mirror freezers, thawing refrigerators, and prep tables process separately the poultry and meat headed up to the galley. Carnival has one supervisor for meat and another for poultry to ensure that no one person ever handles both.

In one room, a pair of crewmen cut fruits and vegetables, with boxes of carrots and cantaloupes piled around them and a work counter covered in bowls of freshly chopped ingredients.

And in one room — in the most staggering room — were potatoes. Boxes of potatoes piled high along every wall, with a diminutive machine in one corner to peel them, and a small work table in the center. They called the worker there Potato Man, and his only job is to cut potatoes.

Like all crewmen we met, he works ten hour shifts. Like all crewmen we met, he works seven days a week. And like all crewmen we met, he has a six month contract, and then two months off before the next contract.

So for ten hours a day, seven days a week, six months at a time, he cuts potatoes. He does not trade jobs, since Potato Man is his assigned position. He does not get to try his hand at chopping the occasional cucumber or celery stalk. He just stands at his post, reducing potatoes to edible sizes.

And when his boss introduced him to us as Potato Man, an unmistakably authentic grin spread across his face, and he gave us an enthusiastic thumbs up. He is the Potato Man on that ship, and he knows it.

Most of the crewmen we met had been working those long hours and weeks for decades with the company. And we tourists were there to get respite from a few months of grueling nine-to-five computer work.

They served hash browns at breakfast the next morning, and oh were they delicious.

On Cruising: The Confinement

For our honeymoon we cruised on Carnival Imagination for four days to Cozumel. This is part of a series of anecdotes on the experience.

We’re told cruising isn’t for everyone. Some people love it, while others vow never to return. We assume this family falls in the latter group, based on what we overheard from their table on our last day aboard — a “Fun Day at Sea” while we sailed back to Miami:

Mother: Today we have to stay on the ship all day.
Daughter (age 5): Why can’t we stop somewhere?
Mother: We have to get back to Miami on time.

Daughter: But why are we on the boat?
Mother: Because we have to be here for grandma and grandpa’s anniversary.

Oh, the noble sacrifice you’ve made for their happiness! Perhaps they took some consolation in the all-chocolate feast laid out just a few hours later. Nobody can be too miserable when they’ve got ten different pieces of cake in front of them.

On Cruising: The Destination

For our honeymoon we cruised on Carnival Imagination for four days to Cozumel. This is part of a series of anecdotes on the experience.

Our ship stopped first in Key West, but we stayed aboard and enjoyed massages at the spa and other onboard luxuries. When we got to Cozumel, though, we raced to disembark as fast as we could say, “One giant bottle of water, please.”

Even walking down the deepwater pier toward the port at San Miguel, we marveled at being on foreign soil for the first time — discounting a visit to Montreal as “barely foreign at all”. Our eyes picked out every detail identifying this new place and making it distinct from our home. And what were the first signs we were able to read? Starbucks! Burger King! Welcome to Mexico.

Just beyond the pier is a small shopping district (“Cozumel’s only shopping mall”) catering blatantly to the cruise ship crowd. One or two men — exclusively men — stand outside each store beckoning passers-by to sample their wares. “Maps of the ruins! Rent a scooter to see the ruins!” were popular enticements. And my favorite was when we were caught leaving one store and skipping the next: “It’s my turn now! I have something different for you!”

A few stalls christened themselves “The Dollar Store” and tagged all their merchandise with hand-written $1 USD stickers. More legitimate businesses quoted prices in pesos, but every business on the island accepted pesos and dollars interchangeably.

If a stall wasn’t “The Dollar Store” it likely had no prices at all, making everything negotiable. When we saw one man selling woven name bracelets and spotted a “Sophie” in the mix, we asked for a price. $12. And a moment later: $10. And when we put it back down, $8.

And when we walked away and saw nine more men selling the same bracelets? $4. Welcome home, Sophie! We got you a bracelet in Mexico!

At the appointed hour we lined up for our tour of the Mayan ruins with our guide Mimi, and our group marched back through the shopping mall to our bus. The place was transformed. The pairs of men still sat on stools beside their shops, but nobody made a move or uttered a word. They know that nobody can entice even the weak away from a tour group.

The Mayan ruins at San Gervasio offered a chance to see and touch and explore history in a way no textbook photography or classroom filmstrip could ever emulate. Some of the forgotten history has been hilariously substituted with wild speculation (“we don’t know what this was, so it was probably ceremonial”); but when you see a rocky road stretching off toward the distant ocean, met at the town’s entrance by a great stone arch, its purpose is hard to misconstrue.

With the sense of ancient history comes also a sense of a truly different place. Rain forest surrounds the ruins on all sides, and more than a few iguanas lounged beside the path as we passed by (some eyeing the tourists with familiar indifference; others fleeing at the sight of us). Even on a cloudy day, the temperature was easily 90°, and only a potent insect repellant (evidently not available in the United States) kept the mosquitos from eating us alive.

Follow that historical adventure with an hour to read on the beach, sipping a “Coca-Cola Light”, and dipping our feet into the impossibly blue water of the Caribbean ocean, and we’ve got ourselves a vacation.

On Cruising: The Budget

For our honeymoon we cruised on Carnival Imagination for four days to Cozumel. This is part of a series of anecdotes on the experience.

The basic appeal of a cruise is that it’s an all-inclusive getaway. With your ticket you get round-trip transportation to one or more vacation destinations, lodging, meals, and a variety of entertainment. Just choose a sail date and a ship and your entire vacation is planned.

The reality is that quite a lot isn’t included. Alcohol is clearly the biggest seller on board, running $7 to $10 for most drinks and available everywhere. Soda, espresso, and other beverages are also upsells — only tap water, coffee, lemonade, and iced tea are included. And with a 15% gratuity added automatically to every purchase, ubiquitous waiters are effectively working on commission to sell those drinks.

Not thirsty? Buy a commemorative picture of your vacation taken in the dining room, on the pier, or in front of staged sets and backdrops throughout the ship. A 5×7″ print costs $10 with a variety of framing options and photo albums available. Or order a heart-shaped “Happy Honeymoon” cake, visit the on-board shops to buy gold chains by the inch, book a shore excursion, schedule a massage at the spa, or play some Blackjack at the casino.

We never felt pressured to make any purchases, but the opportunity was omnipresent. We had budgeted some extra expenses and we went through about $40 just in coffees, sodas, and bottled water to drink in Mexico. Other guests, though, seemed to have sticker shock upon seeing their final bill on debarkation day. On a cashless ship where room keys serve as charge cards, it must be easy to get carried away.

This all sounds much more unpleasant than it really is. Most of the ship’s amenities really are included. When we wanted to see a Broadway-style show in the Dynasty Lounge, we just walked in and found a place to sit. We watched two comedians at the comedy club, attended an art auction and a dance performance, and walked in and out of the restaurants about a hundred times. We played several rounds of miniature golf, relaxed in hot tubs, and read books in deck chairs overlooking the ocean. We took a salsa dance lesson and lost spectacularly at a dozen different trivia games.

The real basic appeal of cruising turns out to be that there’s no set agenda, nowhere to be, and nothing important to get done. We didn’t forfeit tickets or give up our seats if we chose to relax by the pool instead of attending a show, and that simple idea is the essential ingredient for a relaxing vacation.

On Cruising: The Passengers

Let’s break the pre-wedding hiatus on blogging with a series of post-wedding anecdotes on life aboard our honeymoon cruise ship: The Carnival Imagination.

Our first morning aboard the ship we awoke to the breakfast buffet: a sprawling multi-room affair with everything from apples to fried zucchini arrayed across seven separate buffet lines. Passengers happily piled eggs, waffles, sausages, and pastries onto plates to then eat in poolside lounge chairs, at tables overlooking the ocean, or in the air conditioned dining room.

While we waited in a line of six or seven people at the omelette station, another passenger came up behind us. After waiting a minute or so he erupted angrily, “This is ridiculous. There should be two people working here!” And he stormed off.

Yes. You’re standing atop a floating city in the middle of an ocean with a smorgasbord of breakfast foods free for the taking in a poolside buffet under the Caribbean sun, and what’s ridiculous is that you have to wait a minute for your custom-made omelette. As a friend recently remarked: this really is a first-world problem.

Cruise ships are the standard bearer for American gluttony: fat tourists squandering a fortune on drinks, food, and fuel romping about the ocean for sport. Fortunately, only one or two people seemed to fit the stereotype on our ship. When “Formal Night” came, we saw two thousand people walking the deck in ball gowns, suits, and in one case even a tuxedo. We may be gluttonous slobs, but we sure cleaned up nice when we wanted to.