Batting a…one?

Things have been going well for me lately – so well that I cheerfully announced to my husband that I was “batting a thousand”.

Then I stopped to consider what I had just said.

I’m not much of a baseball fan, but I know a few things: when my husband is watching baseball on TV, if all three of those little diamonds are lit up and someone is batting, it’s not a good time to start a discussion. Also, when a batting average flashes on the screen, it’s in the form of a decimal. (Math!)

According to ESPN.com, a website I never had the need to go to until today, the highest batting average last year was 0.341. So apparently this Adrian Gonzalez guy metaphorically batted a thousand by actually batting three hundred and forty one thousandths. (The “th” at the end is how we know it’s a decimal.)

A batting average is calculated by taking the number of times you hit the ball, and dividing by the number of at-bats (since that was the number of times you had the chance to hit the ball). So if you hit every single time you were at bat, you would have a batting average of 1.000. So when you say “I’m batting a thousand”, you really should be saying “I’m batting a one point zero zero zero” or just “I’m batting a one.” But I guess that doesn’t sound as impressive.

It’s interesting to reiterate that the highest batting average last year was 0.341, which means that Mr. Gonzalez (who I’m sure is a wonderful player) hit the ball about once for every three at-bats. Which means two for every three at-bats he didn’t*. And he has the highest batting average!

So next time you have a rough day at work or in life, maybe made a mistake or two, just remember, no one really bats a one (or a thousand, if you insist). The important thing is to get up there and swing.

*Note: my husband launched into a detailed explanation about how the batting average is affected by walks and how hitting the ball is not the same as being credited with a hit, but I can’t summarize it nicely for you because I was snoring.

Math and…aliens?

Last Saturday was the first break from humid summer weather, so I went out for a run. I don’t need to run with my iPod, since my mind provides its own soundtrack. Unlike my iPod though, there’s no variety – the only tracks to choose from are “The Side Stitch Blues”, “Are We There Yet?” “Wow Am I Slow” and “Are We There Yet (Extended Remix)”.

When I do run with my iPod, I usually put on an episode or two of This American Life (a talk show on NPR), since music would still allow my mind’s soundtrack to run.

The episode Saturday ended with a short story informing me there is actually a committee of what our first message to extraterrestrial life would be, should we ever find it. Okay, I know first impressions count, but that’s a little strange. Then they announced what the committee said the message should be. NUMBERS! Yes, MATH is going to be our first message to a different life form. Well, that’s a message I can get behind.

The logic is this: we can’t send them anything that requires context. The Constitution won’t mean anything to them because they a) probably don’t know English b) won’t be able to understand its significance. After all, with no knowledge of our history, it would be like tuning in to a movie mid-plot.

Some argue we should send music as our first message, but again, it’s all context. To us, the beautiful sounds of Vivaldi might be the alien equivalent of fingernails on a chalkboard.

But a binary message composed of all zeros and ones is a message apparently everyone can understand. (Everyone except most people on this planet. I love math and even I don’t speak binary.)

What amused me most was this: imagine what these aliens would think, receiving our binary code? Can’t you just picture them all sitting around the alien equivalent of a well-decorated coffee-shop, speaking in their native tongue, which happens to sound like the most sublime harp music you’ve ever heard, and they can’t stop talking about how they finally reached out to us, and we sent them…math?

It’s funny enough to take my mind off my side stitch.

Gizmo

In May we welcomed Gizmo into our home. He was my father’s cat, and he LOVED my dad. I was worried he wouldn’t warm up to me at all, but that turned out to be a misplaced fear. This of course is a good thing, except for one issue. As you can tell from this photo:

Gizmo is very large for a cat, weighing in at 18 pounds. This is a bit of a problem because he likes to climb on top of me when I’m reading a book or watching TV. When he sees me relaxing like that, he doesn’t think, “Ah, my human is resting after her hard work of providing me with food and all the toys I want.” No, he thinks, “Why isn’t my human petting me?! Some nerve!” Then he promptly climbs aboard and settles down.

Gizmo can sit on me in two ways: the Belly Down position

And the Paws Only position.

Now, I do let out an extra groan when he climbs on my lap and assumes the Paws Only position. In either position, there is still 18 pounds of cat weighing me down, but Paws Only is much worse, and I can explain why mathematically.

In the Belly Down position, he assumes more or less the shape of a 14″ x 11″ rectangle. Which means the pressure on me is 0.12 pounds per square inch, since 18/(14 x 11) = 0.116.

When he assumes Paws Only position, all of his weight is on 4 paws roughly 1″ x 1.5″. This is a groan-inspiring  3 pounds per square inch since 18/(1 x 1.5 x 4).

Hmmm, 3 pounds per square versus 0.12 pounds per square inch – which would you rather have on your lap?

I tried explaining these mathematical concepts to Gizmo. His only response was to meow in a way that made his thoughts clear: “I don’t care. And where’s my favorite toy?”

My birthday present

It was my birthday a few weeks ago! Why yes, I had a very nice birthday, thank you for asking. My sister took the train in, and we went out to lunch and then got dessert at my favorite coffee shop. It was over my steaming mug of tea and chocolate-covered pretzel that she presented me with a beautifully wrapped gift.

I thought at that moment I had everything I needed in life to be happy (notably, a steaming mug of tea and a chocolate-covered pretzel). But my sister knew, in a way only sisters can, there was a void in my life.

A void exactly the size of one (1) math clock:

Naturally, I got very excited about this present. Perhaps a little too excited, because as I gazed at it in rapture, I immediately noted that I had few mathematical quibbles with the clock.

In the 7 o’clock place is the equation 52 – x² + x = 10. However, this equation actually has two solutions: 7 and -6. (You can tell this by factoring:                        -x² + x + 42 = 0; x² – x – 42 = 0; (x+6)(x-7) = 0; so x + 6 = 0 which means x = -6; and x-7 =0 which means x = 7).

Of course, because the equation is on a clock, we can assume the solution x must be 1 < x < 12, which means we can discard the -6. But sometimes it’s fun to be just a bit persnickety.

My other issue is the equation in the 9 o’clock position, which is 3(π-.14). First of all, for the love of math, PLEASE put a zero in front of the decimal point. It’s just considered good form, as it draws the eye to the decimal and ensures it will be noticed no matter what: bad handwriting, a misplaced erasure, or a lazy clock-reader.

But there’s a bigger issue here. As the folks at Wikipedia summed up so nicely, “π is an irrational number…its decimal representation never ends or repeat”. In other words, π does not equal 3.14, it equals 3.141593…and many many more decimal spaces. So the equation in the 9 o’clock space does not equal 9, it equals 9.004779… o’clock. So you’ll be running 17.2 seconds late for that 9 o’clock appointment if you go by this clock. (Since 0.004779 hours * 60 min/hr * 60 sec/min = 17.2 seconds)

Needless to say – or maybe it needs to be said now – I love this clock. My critique was merely a way to luxuriate gloriously in a hearty math debate, the way sports fans dissect their beloved team’s game the next morning. However, after I finished my running commentary it occurred to me I was being a bit rude. Nothing like giving someone a gift and have them point out with joy all the flaws it has!

However, a glance at my sister’s face showed she had taken no offense. Maybe it was my obvious passion and love for both math and this math clock that put the smile on her face.

Or maybe she had no idea what I was saying, and had zoned out to her happy place.

In either event, thanks for the great gift! I am one math clock richer, and a very lucky woman.

The math of Facebook comments

My favorite Facebook feature is the status updates section. (In fact, I’m so old I remember when you could opt to view ONLY status updates, and ignore everyone’s Farmville activity!) It used to be that the most economical way to keep in touch was to write letters – all of 13 years ago – so I get a kick out of knowing what my extended family and friends are up to on a daily basis.

I usually post a new status update once a day, and have found the number of comments I receive on a status can vary wildly. Mathematically, I find this interesting. I suspect positive status updates get more comments than negative ones, but I hesitate to accuse my dear (Facebook) friends of being fair-weathered. Still, people didn’t have much to say when I had a nightmare, but couldn’t wait to encourage me when I was painting my living room.

To examine this hypothesis, I calculate the average number of comments I get on a status update: eight comments. (3+7+19+11+3+3+3+8+10+1+2+3+16+6+13+11+7+14+7+7+2+9+13+6+15)/25 = 7.96 and round to the nearest whole number).

Then I look at the outliers in each range. Which status updates were the real heavy hitters? These had an above-average number of comments:

I’m going to Home Depot at 6 a.m. tomorrow to buy paint.

How many bananas a day is too many bananas a day?

Seeing the band Rush tonight!

Oh Dad, I miss you and have so many questions for you. Most pressing on my mind: did the cat drink out of the toilet when you had him?

One thing I notice looking at this list is these status updates aren’t necessarily “positive”, showing my original hypothesis is incorrect. What they do have in common is that I’m either writing about something unusual (I don’t get to see Rush, or buy paint at 6 a.m., everyday) or I’m asking a question.

These status updates generated very few comments (cue sound of crickets chirping):

I just took a two-hour nap and it was glorious.

Just got back from the gym.

Again, my hypothesis is incorrect – the above updates aren’t negative, they’re boring. A weekend nap by definition is not very exciting, and going to the gym? Why don’t I just post about my flossing regime while I’m at it?

So I can rest assured my close-knit group of friends simply has more to say if I either ask them a question, or do something that breaks from the everyday routine of our work-a-day world. Which reminds me of older forms of communication. Back when I had to pay ten cents a minute to call someone out of state, I certainly didn’t call to tell them I went to the gym or took a nap.

I called to ask them a question or to tell them about something unusual.

Gas tanks

I had taken a bit a hiatus in posting. In my last entry, I mentioned my father was ill. Unfortunately he was diagnosed with cancer, and a little over a month later we had to admit him to hospice. For those of you lucky enough to not yet know what hospice is, it’s care for the terminally ill.

I drove up to see him the day after we admitted him, and my low fuel light came on. I loathed to stop for gas — time was of the essence! I was only two miles away, so I made it to the hospice, clipped on my visitor pass, and spent the day sitting with him.

My husband drove up that evening and met me there. When I mentioned my low fuel light was on, he said casually, “Oh, that’s fine, you have a mile or two of fuel left.”

A mile or two?! That wouldn’t get me to the next gas station! With white knuckles I eased out of the parking lot and coasted to the closest pump. When I got there I noted how many gallons it took to fill up: 11.453 gallons.

According to various sources on the internet, my gas tank holds 12.8 gallons. Considering I get 26 miles per gallon, I actually could have made it 34 more miles (since [12.8-11.453]*26 = 34.32]). That’s good to know, though I hope to never cut it that close.

I’m sad to say just a day after my gas adventure, my father passed away – six weeks to the day he found out he was sick. I could wax mathematically about life expectancies, quality of days versus quantity of days, or how I hope to see him again when my time comes…but if you will forgive me, I will end with a borrowed verse of a poem:

“Even as I am heaving sorrow I know

counting the years will cost me too much.

So I embrace my grief this early morning

I do not want to waste the time I must wait.”

Miss you, Dad.

Coffee beans and math

My dad had a backache last week, so he went to the doctor. First the scale showed he lost 30 pounds in the past month, which clearly wasn’t right. The scale must be broken! Then they took his blood pressure, which was 60/40, which clearly wasn’t right. The cuff must be broken!

No, it turns out my dad was broken. The doctor called an ambulance and sent him to the hospital – his blood pressure was so low it wasn’t safe for him to drive. He left me a voicemail asking me to drive up the next day to feed his cat. (The man has his priorities!)

Visiting hours didn’t start at the hospital until 11 a.m. the next morning, but I was so anxious I was all ready to go an hour too early. I went to my favorite coffee shop, Take 5, to brood over a cup of tea.

As soon as Bernadette took my order, she put an entry form in front of me. They were having a coffee-bean contest! Guess how many coffee beans were in this jar:

And you win this chocolate gorilla:

Well…that sounded like a MATH PROBLEM to me, and nothing cheers me up like doing some MATH!!

Using a tape measure (which is allowed by the rules!) I measured the circumference and height of the jar, and made the following back-of-the-envelope (back-of-the-entry-form?) calculations:

I calculated that the volume of the jar was 170.7 cubic inches, and the volume of a coffee bean was 0.0293 cubic inches. I figured there were five thousand eight hundred twenty six and a half beans in the jar.

I thought math would get me in the general ball park, but there were so many potential sources of error (coffee beans vary in size, there was also air in the jar between the beans, my measurements may not have been spot-on accurate) that I really wasn’t sure how close I would be.

Imagine my excitement when the final bean was counted and I finished in second place! I was only off by 66 beans – there had been 5,761 beans in the jar. Someone (whose favorite number was seven) guessed 5,777 beans and walked away with the chocolate gorilla. But that’s okay, as a runner-up I was awarded:

…gift certificates for a free cup of tea!

But what I really want to know is…who counted all those beans?!

The math of gift-giving

It’s hard to believe Christmas was only three and a half weeks ago. I really enjoy the holiday season. I actually shop for gifts all year long – if I see something that would be perfect for someone, I buy it and put it in the “gift bin” in the closet so I can find it in December.

So it was with horror that I heard about the book “Scroogenomics: Why You Shouldn’t Buy Presents For The Holidays“. Well, the title gives you the premise of the book. (Why not kick puppies while you’re at it?) Author Joel Waldfogel presents the argument that giving gifts is economically (and therefore mathematically) unsound, because a gift I give you will probably be worth less to you than what I paid for it. Therefore, to avoid this, I shouldn’t give any gifts.

To that I say: phooey.

I do understand his argument. One of the gifts I gave my husband this year…actually, let’s not use him as an example because he is so easy to please, it would never occur to him to dislike a gift. Let’s say I bought a sweater for my friend for $30. It could be the wrong size, it could be “not her color”, it could be hand-wash only when she’s a machine wash gal. In which case, I’ve “wasted” $30 and the Salvation Army will be up one sweater come December 26th. But there are two flaws to this logic:

1. She’s my FRIEND, which implies if I do buy her a sweater, I will know her size, what colors she wears, and her laundry habits. Being wrong on one of those doesn’t mean I shouldn’t give gifts, it means I should pay more attention to my friendships!

2. Even if there is the occasional gift strike-out, where what was given isn’t worth what the gift-giver paid for it, the opposite can also be true. I’ve been given a number of gifts that I value much more than what was paid for them, because of the thought that went into it. It’s touching when someone presents you with a gift that demonstrates just how well they know you.

For example, I went through most of 2009 without an umbrella, because the one I owned broke. Did I ever get around to buying myself a new one? No, because frankly, who really feels like shopping for an umbrella? So I just got wet and cursed the fates every rainy day that year. Imagine my utter delight when I opened a present from a friend that Christmas:

Now every time the forecast calls for rain, I reach for my polka-dot umbrella, think of my friend, and smile.

You can’t put a price on that.

Bumper Sticker

My last car hit 133,000 miles before my dad totaled it. That sounds a lot more dramatic than it actually was. In truth, he got into a fender bender, but since the car had a blue book value of $300 – well, you can guess the outcome of that. (I know people who own shoes more expensive than that!)

The point is, I drive cars until they die (or are totaled). So now that my current car is 9 years old, I want a way to dress it up at a minimal cost. Enter: the bumper sticker.

I’ve had bad luck with previous bumper stickers. One bumper sticker I had said “I believe in life before death”, which I thought was just a fancy way of saying “Seize the day”! Apparently I was the only one who thought that. People interpreted it various ways, including 1) pro-life 2) anti-religion 3) against reincarnation (?).

So I plastered the bumper sticker “Kill Your Television” over it. At the time I didn’t own a TV and never expected to have one. But within two years I found myself with a husband, and I never expected to have one of those either! My husband was against killing televisions – he wanted them to live, specifically in our apartment. Off came that bumper sticker.

Last week the obvious solution struck me: the math bumper sticker. And there is quite a selection at Zazzle. I found this very heartening – there are others like me in the world! I was taken with the bold statements of some of them:

but wanted my bumper sticker to have a little math humor involved. So I picked this one:

See, there is no square root of -1, because there is no number you can multiply by itself to get -1. (1 x 1 = 1, but -1 x -1 = 1 also). So the square root of -1 is an imaginary number, written as “i”. So this bumper sticker  is saying “I love math”.

And I do!



Math hotline

Thursday evening my phone announced I had a voicemail and a text. A friend was asking if I knew calculus. Back in my day I was quite the calculus student, however “my day” was (ahem) over 5,000 days ago. But apparently someone with a calculus final tomorrow was having trouble with center of mass problems, and frankly I don’t possess the self-restraint to walk away from any sort of math question.

I called my friend back, who was at her friend’s house, whose stepdaughter was on Skype. The connection was about as good as when we played ‘telephone’ as children, so my friend’s friend’s stepdaughter and I finally just called each other. She read me the problem, which I jotted down and quickly turned to my calculus book.

Here’s a telling fact about me: we moved 8 months ago and I still don’t know where half the stuff I own is. But I can locate my 17-year-old calculus textbook in 5 seconds flat. I keep it prominently on my bookshelf for sentimental reasons, the way a middle-aged man would still wear his varsity jacket, years after it is appropriate to do so. (Well, I was a mathlete in high school.)

After a few minutes I (miraculously) was able to explain the best way to approach the problem. Halfway through the explanation she said, “Oh! I get it now!” Thank heavens, because we were quickly approaching my “limit” of current calculus knowledge (horrible pun intended!)

I hung up the phone and my husband, puzzled, asked, “Who were you helping with math?” I stopped and said, “Um…I have no idea!” and we both started laughing.

One of my favorite quotes is “A teacher affects eternity, you can never tell where his influence stops”. Because I’ve had such a good teachers, enough knowledge (and more importantly: passion) had stayed in my brain to help my friend’s friend’s daughter – and frankly, any one else who crosses my math path. Maybe one day someone I helped will be able to help someone else. It’s paying it forward, math style!