Wednesday, September 30, 2009

Crimes and Misdemeanors

So this is my last post that is part of my September challenge. So I'll definitely be taking a bit of a break after this to recharge a bit! But still, it's been fun!

So the last movie I will write about on this Wednesday is Woody Allen's 1989 picture Crimes and Misdemeanors.

Personally this is my favorite dramatic (but at times funny as well) Woody Allen movie. It revolves around many themes I'm interested in, and really leads to a satisfying conclusion.

I think some may not like it, perhaps those who believe there is a certain order in the universe, karma if you will. But this film reflects the reality of the human condition, the real consequences of our actions and the results of our aspirations better than almost any other movie I've seen.

And so this is one of those movies I always love to show someone if they haven't seen it before, and then you get to talk about it again and again afterwords. Those are truly my favorite movies, the ones that start conversations, discussions, and debates.

I don't want to spoil it too much, but here's the initially lighthearted trailer that gives you glimpses of what is at the dark heart of this movie. Give it a watch, you'll either like it, or it will bug you like crazy, but I doubt you'll be neutral about it.

Tuesday, September 29, 2009

My last September ramble

Whew - it was a heck of a month to take a daily blog writing challenge.

Having my job situation go through such an upheaval and my commuting substantially change made it even more of a stretch to write a blog entry every day.

A few days I was at a loss at first for ideas, but most of the time I could think of something to write about. The hard part was that often I thought of something to write about that just couldn't be done well in one day.

So I'm looking forward to going back to a slightly different publishing schedule, but I should maintain the habit of writing every day.

Although I write and publish these blogs out on the web, ultimately they're for my kids to read when they get older. By publishing them instead of writing privately, it drives me to make the pieces cohesive and meaningful. (At least I hope that's the result!)

So one last film to write about tomorrow, hmmm. Still thinking about it.

But thanks Elsa and Laura, for the challenge. I think it was worthwhile to give it a go. Just one more day!

Monday, September 28, 2009

I want to grow up to be...

When my oldest son was around 6, we were chatting and suddenly he said to me...

"When I grow up I want to be a woman!"

On the outside I remained calm, but on the inside I'm going - whoa! Where is this coming from?

So I asked as naturally as I could "Oh, why's that?"

He said - "So I can work where you do!"

"Oh!" I said, feeling a great deal of relief. And I explained "There are plenty of men who work were I do, so you can grow up to be a man and work there too."

"Oh, OK, then I'll grow up to be a man!" he said.

I still smile when I think of this, and I absolutely cannot wait to tell him this story later. I'll have to pick my timing well. :)

Sunday, September 27, 2009

How long will it take?

There's an old Abbot and Costello joke where Costello describes a problem he's having. I've always liked this joke because of what it's playing around with mathematically.

Costello tells Abbot he has a problem. That he likes this girl, but she's only 10 and he's 40, she's 1/4 his age. So of course he can't have anything to do with her yet.

But if he waits 5 years, she'll be 15 and he'll be 45, so she'll now be 1/3 his age. Still not good.

But if he waits another 15 years, she'll be 30 and he'll be 60, she'll be just 1/2 his age!

So, he wonders, how long does he have to wait before they're the same age?


Saturday, September 26, 2009

The relativity of years

Just a short philosophy post today.

I always remember summers seeming to last forever as a kid. As I've gotten older it seems the years fly by. I decided a long time ago it had something to do with the proportion of time you had already lived.

When you're 5, a year is equal to 1/5 the life you've already lived, so it seems relatively long. When you're 50, then a year is just 1/50 of what you've already lived and so by comparison seems much shorter.

A history professor I had told me that was a mathematician's answer, perhaps meaning it wasn't a very appealing explanation. Personally, though, I always got a kick out of thinking of it this way.

Friday, September 25, 2009

My gaming notebooks

I keep notebooks on video games I play. They're tabbed and organized with checklists and various notes and goals.

Where the kids want to move on, I want to find every item, quest, explore every location, etc. And optimize how I do all that as well. I can't remember how many times the kids have urged me to move on when they're watching me play, but I've got to find that last banana!

Now games come and go, and I usually toss stuff I've done for games I don't play anymore, but the kids ran across a notebook I had made for a game I played quite a bit a few years ago. My husband told me how they paged through all my notes in awe with my oldest remarking "Wow, she's really thorough!"

It just satisfies something for me to do these things to this level of detail and completeness, and of course I love figuring out new games. But I think it all stems from the reality that I can't do that for most things in the real world.

I can't test software as thoroughly as I want, I can't keep the house in the state I want, etc. etc. And so instead of getting frustrated in real life, I grind out this urges in games and it's probably a big part of what keeps me playing.

So there's clutter in the living room, there are a bizillion things I can think of to torture the product I'm qualifying that I don't have time for, but I can max out my blacksmithing skill for my level and find all the possible patterns I could make and feel content.

Thursday, September 24, 2009

The orange glow in the night sky

I grew up in a factory town. There was a huge paper mill that polluted the local river. And there was Armco Steel, a huge steel mill.

At night steel that had been formed into huge blocks was left outside to cool. It still glowed orange from the residual heat. So sitting on this rough concrete supporting wall at the side of the old victorian we lived in you could see the orange glow in the skyline.

It's one of those things I still remember clearly, my bare feet against the angled top of the retaining wall, the incredible humidity of southern Ohio, the black sky and the orange glow.

The paper mill no longer pollutes the river, and the steel plant is no longer in business. I go back and visit since my brother still lives in the house, but it's funny. I never really understood the quote "You can never go home again" until I've gone back and visited home, seen how much it has changed, and realized that that reality is gone, it's something my kids will never see or experience.

It wasn't all good, and it wasn't all bad, but it was what I grew up with. And when I think about it, it makes me wonder what is it in the kid's reality that will fade away in the future, but will stick with the forever. That they'll wish they could bottle up and show their own kids.

Wednesday, September 23, 2009

Can I be excused, my brain is full!

So I can tell I'm frazzled. Instead of a ramble yesterday, and a movie write up today, I did the movie yesterday in a rush.

My company was acquired and I've been in orientation all this week, and my head is swimming with all the information that's been thrown at me.

So I'm trying to come to grips with what's going on, and it's really a good situation. How can I complain, I've been continuously employed for more than 15 years. Considering what's happened in software in that time, that's not bad. And considering the current economic times, it's even better!

So I'm jumping in over my head, hopefully I'll come up swimming like I usually do and I'll get some enjoyment and great experience from this new opportunity.

At the same time, since I'm planning to retire in 11 years, as much fun as this might be, I'm ready to settle down with a company. I would prefer to have been somewhere more than 5 years leading up to retirement. Will it be this one? I hope so!

Tuesday, September 22, 2009

Good Night, and Good Luck

Sorry ahead of time for this short movie write up, but I've just had a job change through acquisition and so am finding myself a little short on time.


With the squawking headlines, ratings grabs and unbalanced presentations you see now, it pales in comparison to what it took to really shed light on the paranoia that was going on back in the 50s.

With the state of journalism being what it is now, it's worth watching Good Night, and Good Luck to see what it takes to expose the distortions and abuse of power that was going on at the time for what it was.

Would that we could have such effective reporters now. I can only hope it will get better in the future, but for now watching this helps fire me up and keep me tuned into what kind of bravery and rationality in face of intimidation it takes sometimes to do the right thing.

Sunday, September 20, 2009

When polynomials go wild

Every fall I took an advanced problems seminar starting with my 2nd year of undergrad. In that course the professor took problems or variations of problems from the Putnam Competition to prepare a team for the university.

This problem is not from the exam, but is related to an exam question and was presented to us in this course.

A polynomial in a single real variable is a very well behaved function. It's easy to find its minima and maxima, and you know that it happily charges off to infinity or negative infinity as you give it bigger and bigger positive and negative numbers.

But the problem that was posed to us one year was this - can you create a polynomial in 2 real variables that has the range (0,inf). Note that the range asked for is NOT [0,inf]. You need to create a polynomial in 2 real variables that you can show gets as close to zero as possible, but never attains it.

Although most mathematicians might solve this pretty quickly, I remember tinkering around with the problem for a while playing around with the relationship of the 2 variables to take slices of what would be a surface. As I had lunch with one of my professors I described the problem and told him how I was playing around with it.

I explained that no matter how I sliced the surface I didn't seem to be able to create an equation that had the desired behavior. I described how I made the slices of the surface - by substituting a linear relationship between the two variables when it hit us both at the same time.

By looking at slices like this, I was always reducing the problem to a polynomial in 1 real variable which would NEVER exhibit the behavior I was looking for. We both knew it was the key to the problem.

I started playing around with the a relationship between the two variables, and not long after that I had created my function and was able to prove it had the range (0,inf).

I'll update this entry later with one possible answer, but I'll let you play around with the idea yourself for a while.


Saturday, September 19, 2009

Assuming you don't know why

Every once in a while I'll catch myself suspecting someone of ulterior motives in their actions, and it's almost always in a negative way. Was that a back-handed compliment? Are they trying to point out a mistake I've made? Etc. Etc.

Over time I've come to realize that that's almost never the case. In fact the vast majority of what most other people do has very little to do with me personally. It's actually quite a self-centered point of view to think that it does.

So whenever I catch myself thinking this way, I always try to take a step back and assume I don't know why they're behaving that way. I think about what my intent would be making the same statement, or doing the same thing. And then assume that it's likely that someone else's intent would probably be the same or very similar to mine.

Sure, I've run into people with bad intent, and with motives I would never have, but most of the time I realize that I'm taking something personally when I shouldn't. And I've found that over time, it's been better to err on the side of considering other people's behavior generously than to do otherwise.

Friday, September 18, 2009


I have to admit to liking the more quirky games in general. In particular I really like games that have a more collaborative feel and where you need to figure things out better that straight shoot 'em up type games.

As soon as it came out I picked up Pikmin for the Nintendo Game Cube and I wasn't disappointed.

You're a stranded astronaut who needs to repair his spaceship to get back home. You have to find all the necessary parts that were scattered when you crash landed and the game provides some interesting challenges w.r.t. to getting these pieces. This is fun and interesting to figure out, but it's how the game is played that give it it's charm.

Instead of slaughtering anything in sight like so many games, in Pikmin you develop a mutually beneficial relationship with the natives. You can recruit up to 100 of these cute creatures and they'll follow your every command and aid you in your quest.

But with power comes responsibility. Your little helpers can be killed by monsters, drown, get electrocuted or burn up, and in the process of dying they emit the most pitiful wailing sound that will make you feel like a heel for allowing it to happen.

So these little guys are not dispensable little robots, but little friends you feel responsible for and will try your best to keep them all alive and healthy. Every time you hear one of those dying wails you want to start over from your previous save to see if you can complete your task without losing any of them.

Pikmin 2 came out later and introduced even more collaborative play as well as a player vs. player mode and now they're being updated for the Wii. Even better Pikmin 3 is rumored to be waiting in the wings and will take full advantage of the Wii controls which should be really interesting.

I'll tack on some videos here in a little while to give you a feel, but if you've got a Wii or Game Cube it's worth trying out this game.

Wednesday, September 16, 2009

The Iron Giant

If you've enjoyed "The Incredibles" and "Ratatouille," you need to go back and watch Brad Bird's first move "The Iron Giant."

"The Iron Giant" came out in 1999 to little fanfare, but the preview caught my eye and I went to see it with my oldest son who was just 4 and my mom who was visiting at the time.

Kids will enjoy this movie for the fantasy of having a giant robot for a friend, but just like Brad Bird's other movies, there is so much going on here, the movie is so rich.

We see the red scare paranoia of the time, the reckless actions of someone who is arrogantly certain of themselves, and yet we also see military people who are sensible and can listen to reason. Questions about the meaning of life, about the idea of having a soul come out of the boys relationship with the giant.

Add to that great visuals, and one of the earliest mixes of hand painted and cgi animation and it's not just a great story, but presented beautifully as well.

But the biggest message, and one that I love this movie for, is the exploration of the idea that you choose your actions and define yourself by them. That you do not have to be what others have tried to define you as.

Unfortunately the trailer available online at IMDB is not the original trailer, and I didn't care for it. If I can find the original trailer I will link it. (Found it, here's the original trailer, much better than what's on IMDB now Iron Giant original trailer.)

If you get a chance to watch it, I hope you enjoy it as much as I did. It's also worth reading about why Hughes, the author of the original story this is based on "The Iron Man," wrote the story in the first place. I leave that to the reader to explore.

Tuesday, September 15, 2009

A contrast in protests

This is my ramble day, so I'm just going to write a little about something that caught my attention yesterday morning.

Two examples of protesting in the news:


A few anti-health care reformers carried weapons visibly to protests they participated in. Completely legal in their respective states.

Yesterday morning I read the story of a motorist facing 90 days in jail for honking in support of a protest against a congressman since the state law is that honking your horn is supposed to be for emergency purposes only.


Although carrying the gun to the protest and carrying it visibly is legal where these people did it, I know exactly how I'd feel if I was on the opposite side of that protest (and I am). I'd be intimidated, I'd worry that if I said something that caused a strong reaction by this guy I might be endangering myself and those with me. I personally find it chilling.

The second case, although it is strictly illegal to use your horn that way in that state, people use their horns to support protesters they agree with all the time and everyone honks to catch the attention of people they know, this goes on everywhere. My bet is an examination of the use of this law will show that it is almost never applied. So my guess is in this case a law is selectively applied by those in authority for political reasons.

What's my point? I don't know, that's why this is a ramble. I do know that I personally would not try to suppress someone else from speaking out for what they support even if I disagree (obviously there are some boundaries I would have issues with too though perhaps it's the perception of where the line gets crossed that is the core of the problem?)and I would personally rail at a law being unequally applied to me.

I'll have to think on it a bit more before I have something more to say.

Sunday, September 13, 2009

A moment of mathematical delight

In my 2nd year of college, in the midst of taking Linear Algebra there was a homework problem that was just a delight. It opened my eyes to the possibilities and along with taking a course in Abstract Algebra, wooed me away from Systems Analysis and caused me to switch to a major in mathematics.

Up to this point mathematics had had the same flavor. Algebra, Trigonometry, Calculus, I really enjoyed it all. In fact I distinctly remember the Calculus classes feeling like I was being reminded of what I already knew. Computations, numerical manipulations, etc. Certainly there were lots of interesting ideas, but nothing like what was to come.

So then I took a combined Linear Algebra and Discrete Mathematics course. After learning all the mechanics of matrices and such, we hit this chapter that defined vector spaces. That was pretty neat, but the possibilities didn't hit me until I did homework problem number 14 at the end of the chapter.

This is from Howard Anton's Elementary Linear Algebra, 5th Edition. It's a simple enough problem. You had to demonstrate that the following defined a vector space:

The set consists of just the moon. The operations are moon + moon = moon and k(moon) = moon where k is a real number.

This was the first time I'd seen a problem like this. I dove into proving or disproving it was a vector space. As it turns out, it satisfies the definition of a vector space.

All of a sudden there were so many possibilities! This problem showed me what you could start playing with when you stepped away from the real world and stripped mathematics down to the ideas. I wanted to just hug this problem!

This problem had such an impact on me that I still remember it 20 years later, and was able to find the problem in the book in just a couple of seconds.

Much of the mathematics I took later built on this problem's promise and this ended up being the mathematics I loved. Abstract Algebra and Point Set Topology were the areas I savored, and I still like to think about the ideas we played around with in those classes all these years later.

Saturday, September 12, 2009

What happened to rational thinking?

With the internet and the incredible access to information we have now you'd think people would be better informed about what's true, what's myth, etc.

But instead it seems like the opposite is going on. Conspiracy theories run rampant. People repeat what they hear without question. It's really discouraging.

Everyone operates with their particular filters on what they see and hear and only take in what aligns with their point of view. You can now form your own echo chamber in a moment, and cherry pick the kind of news and opinion you want to hear without that much effort.

The internet has now turned information into sound bites (or text bytes?) more than television ever did. And so catchy and provocative phrases win the day over factual nuanced information. It feels like we're getting less thoughtful as a culture, and more and more knee-jerk instead.

I've watched educated, smart people take local isolated observations and assume they apply to the nation as a whole. I've seen others who should know better, who I thought were educated about the use of the scientific method support a hypothesis selecting only information that supported that hypothesis rather than considering all available information. I've seen statistics selectively applied on small numbers and used to puff up a point. Context no longer matters.

People may worry about the economy, and a host of other immediate concerns, but I think the real threat to this country is a lack of a solid education in evaluating information. We've been trained too well to just be consumers rather than thinkers.

Friday, September 11, 2009

The best games surprise you

My favorite moments in video games are definitely when something takes me by surprise, something that is completely unexpected - but is consistent with the game story.

A couple of years ago playing World of Warcraft I had one of those moments that still sticks with me.

In the game when you're out and about you might run into wandering monsters, etc. But once you go into a town, you're generally safe. In particular when you go into an inn, where you typically log out, you're always safe.

You probably see where I'm going here...

So there I was, fresh from doing a few quests and such, I went into a town and into the local inn. I was checking my bags, thinking of what I wanted to do next when there was shouting from the town guards about assassins in the hills. I noticed, but ignored this since I was safely inside the inn and stepped into the kitchen to start doing some cooking when it happened!

Suddenly I was garrotted from behind by an assassin! Right in the kitchen of the inn! I was totally shocked. So now I'm fighting for my life in the place where I'd always felt immune to danger. I had to do everything I could to survive. When I picked up the loot from the dead assassin, one of the things he held was a contract on my life. On me! As it turns out this started a quest where I would find out more about those who put out a contract on my life. It was awesome.

This has been one of the things that has kept me interested in playing World of Warcraft (among many other things) and they've gotten better and better at inserting little and big surprises in the game. It definitely keeps me coming back every day.

Thursday, September 10, 2009

When I walked on people to go to work

When I worked over in Great Britain in the Navy every year we had a group of protesters that came out to protest our presence. They were called the CND, Committee for Nuclear Disarmament.

Now at the tiny Navy base I was at I guess you could consider us a potential target, I guess that was their beef with us.

When I'd have to walk past them to the base they'd yell and scream at us. "Baby killers!" "You're worse than the Nazis at Auschwitz!" I mean it was amazing. These guys don't even know me and they're yelling this stuff at me.

It didn't make me mad, I just stayed quiet and walked on by. Part of what I'm defending is the right of free speech, so have at! I actually loved going to Speakers Corner in London to listen to some of the stuff that was said no matter how much I disagreed with some of it. I thought it was great that people felt comfortable enough to spout off about whatever there.

So this is the usual routine. Getting yelled at by these folks when they came and protested. But a few times they pulled some stunts to try to actually block access to the base. The most dramatic attempt occurred as my watch group was waiting to go in to do our shift

A huge group of these protesters rushed the gate and basically made a human carpet in front of it, the ground leading up to the gate was wall to wall people laying there. What the heck were we supposed to do? I can't remember who it was specifically, but a higher up in charge ordered us to go in. We were to walk over the protesters and go to work.

I have to say, it was one of the strangest experiences of my life. As I ventured through I carefully watched and tried to step on arms and legs rather than other parts, I figured this would be the least painful for the protesters and I apologized as I walked along to the gate stepping on person after person.

Some of my colleagues were not so kind. They hated these guys and took advantage of the situation to take some of that out on them by deliberately stepping hard on them and not caring where they stepped.

It was surreal. I can still picture looking at my feet as I carefully selected an arm to step on while I made my way across. Very Twilight Zone-ish.

Fortunately it was only that one time they tried that. I suppose since it didn't stop us from going in, it wasn't worth doing again. They occasionally stormed the fences of the compound laying carpet across the barbwire and climbing over. It was a huge security hassle and caused us to have to establish security watches and stand out in the cold.

The only good thing I ever experienced due to these protesters was one night standing on the roof doing one of these security watches I saw a barn owl glide across a field and land on a post. It was amazing. So quiet and large, it was all white and looked like a ghost as it floated over the field in stark contrast to the black night sky. It disappeared back into the dark just moments later, but left a permanent image in my head.

So these are two of the memories that have stuck with me from those days and what a contrast they are. One of ugliness and strife, one of calm and beauty. And yet I would not have seen the second if it hadn't been for the first.

Wednesday, September 9, 2009


During what would normally be a very dramatic moment in most movies I was cracking up. I leaned over to my friend Elsa and whispered “An alligator is going to eat one of these guys!!” with absolute delight.

This wasn’t an indictment of the movie maker’s skill, it was an appreciation for it. Everything that had been foreshadowed earlier in the movie was being delivered on in full and beyond.

It’s interesting because in many reviews I’ve read of Adaptation, the major complaint is that the first two thirds are great, but that it falls apart in the last third. As a whole it seems these folks didn’t catch what was happening, how the movie was modifying itself as we watched, adapting, and making itself more commercial. Fulfilling the original screen writer’s worst fears, but following the advice he received in the screen writing seminar. From the moment he brings his brother on board to help the movie includes everything he listed in what he didn’t want the movie to be about. But it succeeds is wowing them in the end.

So Adaptation has ended up being my favorite movie of all time because of this and many other things.

It's the story of two brothers - one paralyzed by concern of what other people think of him, living a life of extreme introspection. The other oblivious to the opinions of others and who gives no thought at all to what he does.

It's the story of a person who's passion is extreme and temporary and moves from one thing to another with no permanence in his life, and a person with no passion for anything.

It's about adaptation, not really the Darwinian kind, but the kind we all go through every day when we interact with each other. How we adjust to our circumstances to just get by. It plays with so many ideas that I'm fascinated by.

And it begins with one of the most amazing monologues ever in a movie.

Just writing about this movie makes me want to watch it all over again. Although it's not to everyone's taste, if you do watch it I hope you enjoy it as well. Here's a link to the trailer, enjoy!

Tuesday, September 8, 2009

First Real Ramble for September

So I'm going to just blop out some thoughts that have been swirling around in my head this past week, and try to limit myself to just a few sentences each.

I firmly believe now that cell phones and texting are leading people to be less and less connected to what is going on around them. There seems to be this fear of silence, of just having time to think.

The media no longer makes people prove or support their claims. For any information put out by groups or individuals, when the media brings these people on they should question the basis for the claims. Anyone who has a valid argument or idea should be able to walk us through the steps that got them there, and clarify what is based on concrete evidence, and what is speculative. Instead all claims are published and given equal validity and not questioned as they should be.

During the past 10 years I feel like I've seen tactics previously used by the Soviet Union adopted in the US. Disinformation, torture, the inability to challenge your own detention, indefinite detention. We denounced these tactics then and they were part of the reason we held the high ground in the Cold War. I firmly believe the ends do not justify the means.

My 70 year old mother's car was defaced because it had an ACLU sticker on it.

Saw for the first time one of the nebulas in Orion with our telescope with my 10 year old son.

I've listened to the history of the 5 great religions: Christianity, Judaism, Islam, Hinduism, Buddhism. In all cases if individuals lived by the philosophy if their religions, the world would be a beautiful place. But what became apparent is that the vast majority of adherents of these religions do not do that.

Every US citizen should live outside the US for 2 years to avoid the myopia that develops from growing up in the most amazing and privileged country in the world. I think people have no idea how good they have it here, but also have an unbalanced perspective because they've never lived anywhere else. Everyone would learn a lot by living outside the US for a couple of years.

I get teary-eyed every time I hear the national anthem. I served my country for 6.5 years during the Cold War and feel very strongly about that. And I'm a liberal. Being liberal doesn't exclude being patriotic.

I've come to the conclusion that people who try so hard to force their views down other people's throats, basically feel like it's my way or the highway are fundamentally insecure in their beliefs. They only way they can feel their beliefs are valid is if everyone else believes the same thing. That their belief must be "right" and all others "wrong."

Most people operate with good intent. Even those I disagree with. :)

So those are just a few of the things I've thought about the past week! Couldn't quite limit to a couple sentences with some, and some of these may end up being fodder for longer blog entries later. My hope is that at least they're food for thought for anyone who reads this as well.

Monday, September 7, 2009

Mom's Pillow

Maybe around 5 years ago or so somehow my husband and I were talking about me wearing perfume in front of the kids.

To my surprise my middle son piped up in a clearly euraka-like moment and declared "So that's why your pillow smells nice!"

Incredulously I asked him - "You smell my pillow?" And in the most sheepish way you can imagine he softly answered with a slow embarrassed "yes."

I mainly found it amusing, and felt bad that he was embarrassed. I could easily imagine him going up and laying down on my side of the bed and being comforted by the fact it smelled like me, he was only around 6 or 7 at the time.

But it's one of those little memories of the kids I treasure and I can't wait to share with them again when they're grown and have their own kids taking comfort in something that reminds them of their own parents.

Sunday, September 6, 2009

My Favorite Algebra Problem

I have an algebra problem that my adviser, who was also my calculus professor for 2nd semester calculus, showed me one time.

Over time I've grown to like this problem more and more, and I'll explain why after I describe it.

The Problem:

Assume the earth is a perfect sphere. Now imagine a rope tied snugly against the equator. Now take some addition rope and splice in 10 additional feet to the rope and then spread out the additional rope evenly so that the rope is same distance above the surface of the earth all the way around. (Imagine when you have a very loose belt and hold it out so that it is the same distance away from you waist all the way around.)

So now the question. Would you be able to crawl under the rope around the earth then? Answer quickly - what does your intuition say?

The Answer:

The answer is, surprisingly, yes! In fact you will have ~1.6 feet of space to crawl under.

Now I don't know about you, but this makes no intuitive sense to me, 10 feet evenly spread out over such a huge object? But it's true, and here's the proof.

We know the the formula for the circumference is C=2πr where r is the radius of the sphere. So let's call the radius of the earth R. If that's the case, then:

2πR + 10 = the new circumference

Now to determine the height this gives us above the earth we'll use the variable x to represent the additional radius we get, so then we can express the circumference a 2nd way:

2π(R + x) = the new circumference

So now we can make an equation and solve.

2π(R + x)=2πR + 10
Next expand the right hand side

2πR + 2πx = 2πR + 10
Notice the 2πR on both sides - get rid of it

2πx = 10
Now just divide by 2π

x = 10/2π
And we're done, the additional height is 10/2π or ~1.6 feet

This is one of the things I love about math! That something can run completely against your intuition, and you can prove it's true. I love those kinds of math moments.

Even better, this is a cool problem you can do with any Algebra class.

But now for the things I love even more about this problem. Did you notice how the terms 2πR canceled out? Do you understand what that means? That means the size of the original object does not matter. That this experiment would have the same result whether the original sphere was the size of a marble, basketball, earth or the galaxy! Isn't that amazing? That's even more counter-intuitive! You could even have a class try this experiment with different size circles out on the playground to demonstrate this in the real world.

Next is the part that makes this problem all the richer. Once students have learned calculus, you can actually revisit this problem. Now you can look at the formula for the circumference and ask - what's the derivative?

Since C=2πR then the derivative is C'=2π

It's a constant! This shows that a change in the radius is simply multiplied by a constant to determine what kind of change you see in the circumference and the size of the original object is not part of it! Now you have a clear understanding (if you understand calculus) as to why the size of the original object didn't matter.

I hope you enjoyed this problem too. And the next time you see a kid in need of something in mathematics that might intrigue them, now you've got something you can really wow them with.

Friday, September 4, 2009

The Perfect Response

I was goofing around in one of the capital cities of World of Warcraft on my way from here to there very early in the morning (I often play between 4 and 5 AM) when a conversation caught my attention.

One of the things I love about playing an MMORPG in contrast to some adventure game I'd play alone is the game world is alive with real people, and I'm not the center of attention in the story line. It makes it much more entertaining than playing alone on one of my game consoles.

So the conversation goes like this (now this conversation is not private, but those talking are broadcasting what they're saying to everyone in all the capital cities):

One person to some other player: "are you a girl in RL?"
Another: "no girls play wow"
Another: "once they make female sex robots, women will be obsolete!"

I practically laughed out loud and thought of the perfect response...

"If they invent female sex robots, men will be occupied 27/7 and women will take over the world...muahaha!"

Now if I had said this, it would be a dead giveaway that I was a woman. And with that I'd likely have to deal with questions, requests, and who knows what other stuff. Although I suppose if I told them I was a mom of 3 that was pushing 50, perhaps that would have curbed their enthusiasm.

But I refrained and went along my way smiling at the silliness of it all. Perhaps I should make a temporary character just to pop on with to make snappy responses. Hmmm...

Tuesday, September 1, 2009

September Challenge

My friend Elsa this past week brought up a challenge she was taking on for the month of September - to write to her blog every day. She's doing this along with a friend Laura and thought I might be interested in trying as well.

Sooo...I'm going to take the plunge and give it a try. A blog entry a day, we'll see if I run out of things to talk about in a week!

Elsa's blog can be found at: Who Elsa?
Laura's blog can be found at: True Stories, Honest Lies

Part of the challenge is to have a theme for the day of the week. So here are mine:

Tuesday's - Ramble
Wednesday's - Favorite Movies/Thoughts on Movies
Thursday's - Stories of my childhood/life
Friday's - Video Gaming
Saturday's - Life Philosophy
Sunday's - Thoughts on Mathematics
Monday's - Family & Kids

So here goes, this should be an interesting September!