sandokai asked: "What was it like for you doing math as you were growing up-- like what was your relationship with math?"

Growing up I really liked patterns. Mosaics, triangles, building tiny houses out of toothpicks. Dad taught me how to count in different bases of numbers - base two, base eight, I thought that was so cool.

I did not consider myself to be good at math. We had those timed multiplication table tests in elementary school - I stunk. Full honesty, even today if you randomly come up to me and ask what's 8 times 5 there's a chance I will hesitate. Then say 35. Then say 40. Then apologize.

In seventh grade they split us up and some kids would get to take pre-algebra. I was not one of those kids. I was in the average math class. I took pre-algebra as an eighth grader if memory serves, then algebra as a freshman.

My parents thought I was smart and wondered if they should push me to get into a higher math class, but then had an interesting conversation with a neighbor/teacher person. She basically told them that if I took algebra as a freshman, then I'd take geometry, algebra 2, pre-calculus, and then take calc I my first semester of college. That was more than good enough, a lot of college kids have to take college algebra or even remedial math. Those advanced kids were lining up to take calc 2 their first semester of college - not a great idea, since calc 2 is a class that many people agree is the toughest math out there. Some of them see this coming and decide not to take calculus in high school, just take a year off math. Big mistake. Never take a year off math, she said, even if you're ahead.

Besides, math is one of those things that can drive you crazy if you stretch yourself beyond what you're ready for. If you think you're smart enough for advanced class, why not just set back and get As in the non-advanced class? Build some confidence.

That's what I did and that's what worked out. Even though I never liked math before, my sophomore year I realized I LOVED geometry. It was like a whole different world of math! Like learning that spinach quiche and french silk chocolate are both kids of pie. Geometry and proofs were poetic. And I saw myself suddenly getting something that not all the kids around me were getting, I suddenly felt like I was special and had a lobe for something.

In algebra 2 I had a very good teacher who not everybody liked, she came off harsh sometimes, but she explained things in ways I could understand. I suddenly understood notation for logarithms and then logarithms snapped for me, which was a light bulb because I didn't know that my struggles had been about the notation, I thought I just couldn't wrap my brain around how the numbers worked. Once I saw it reframed, I realized again that I could do this. For a little bit I almost thought about being a math major, but the jobs didn't seem all that interesting, I wasn't sure what math majors do.

I liked pre-calc, went to college and took calculus, math started getting harder and more "out there" but by now I kinda understood how I learned and the process of just pausing to ask "What's step 1?" to see how to solve problems. I had to take up to calc II for my tech degree but also took calc III just for fun because I had the textbook and it would get me a math minor. For my masters I had to take differential equations. I needed a study group, but got through in the end.

There's this discussion we have in engineering outreach about math perceptions. Kids think that you have to be a math genius to be an engineer, so at the ripe age of like, 11, they decide they're not qualified. It's sad because at that age you really haven't seen all the kinds of math in the world. You might take to different kinds differently! And honestly, I really do not use much math as an engineer. It's kind of a running joke. It's a little sad. One day a guy in our group got to use trigonometry to figure out a radar reflection angle thing and he bragged about it and we all gathered around like "What! You got to use trig!" We were all excited for him and wanted to hear all about it, even though trig is 10th grade high school math... and here we'd all taken dif eq?

My dad said that an engineering degree just proves that you're "educable" - doesn't actually serve as the basis of the knowledge to do your job. I believe now, after hiring college students, that the degree serves to demonstrate your commitment. People spend their whole lives designing airplanes, you're not going to understand this whole product, and even more important the huge people organization and processes to get it done, in three months. We're going to train you for years. If we're going to invest in training you, we want to know that you intend to work in this field for at least 5 years, if not 40. It's not just a fun thing you're trying. If you had the patience to earn a four year degree in engineering, that's a good sign.

So you don't have to love math to be an engineer, you have to get through it, hopefully you find some patterns and methods you enjoy, but it's like latin, teaches you how things go together and some interesting things to think about.

I read a teacher explain that we needed to learn math for the beautiful sake of it, and I agree. Kids ask when they'll use it, we say "to balance your checkbook!" what a terrible answer. That's like telling kids that they should study art in case they have to paint a house someday. It's a luxury to get to think about everything we have in math, and that's what I appreciated in the end.

I also told Josie, who got a math award in Kindergarten, that math was important because it could prove you were smart. And if people think you're smart, you get to work with them on the coolest projects. That's the story of my life right there, starting with geometry and ending with a fleet of airplanes that fly.

You know how people buy those rolls of raffle tickets, and hand them out, and every ticket has like an eight digit number on it because they're meant for a raffle where there are a zillion tickets handed out but really no group you're at is ever that big?

I hate when the guy on the mic calls out ALL EIGHT NUMBERS of the winning ticket, every time.

If there are 500 people there, you can just call out the last three numbers. Seriously.

Or even better... if there were 500 people there, and you have like 30 prizes to give out, just call out the last two numbers. Up to five people could come up at once, but it's more likely to just be a couple because the others have left, lost their tickets, or just aren't paying attention. Either way your chances of finding SOME winner go up a lot, and that'll make the whole thing go a little faster.

This all runs through my head every single time I'm sitting someplace holding a silly little ticket with a bunch of numbers on it, and I always wondering how bitchy control freaky it'd be to point it out. I'm guessing it'd look pretty bad. I don't know how other people can just be patient on issues like this.

My friends keep giving me crap because at a party we needed some scratch paper, and marc got some out and I immediately said, "Really, all you could find was quad rule?"

They were like, "What the hell is quad rule?"

Marc held it up and everyone agreed it's called graph paper.

Well yeah, but graph paper could be anything... you can graph things on semilog if you want, some people even consider isometric lined paper to be "graph paper".

I did not go into the gory details of the difference here! But I've still be ruled a nerd by this particular group for calling the paper what it is. Just me, or freak group? I hate thinking that it's really not normal to distinguish quadrille, I'll admit I have nerdy things about me but it sucks when you're a nerd without even being aware of it.

I picked up Innumeracy: Mathematical Illiteracy and its Consequences by John Allen Paulos because a coworker said it was just chock full of geeky good fun. And it is! But weirdly enough it rang right in line with the last non-fiction book I read (Lisa Bloom's Think) on the theme that people need to take a little more care to know what's really going on in their world. I totally agree.

The theme is that we live in a world of information and facts. For example, you can find out in an instant that 15 Americans were killed by terrorists in 2010. What you have to decide for yourself is how that number should affect the things you do every day, whether you should be scared, whether you should lobby your government to spend more money fighting terrorists or feeding starving kids (hunger, as it turns out, kills a lot more than 15 Americans a year). And that's where the issues come in. Life is full of risks and probability, but people who don't understand how fractions or percents work aren't enabled to make rational decisions based on what they hear. There are tradeoffs. There's a cost-benefit. Do you want a higher speed limit or fewer traffic fatalities? Safer environment or cheaper toys for the kids?

The book runs through lots of entertaining examples of problems involving numbers, and the point is that they can be solved! There is a way! I don't think we all need to memorize every method, but it's important to just know that the tools are out there. Do you need to find out how likely you are to eat pizza, given the fact that you're an America? Conditional probability! If you lose $100 every time heads comes up on a coin, but win a billion if tails comes up twenty times in a row, should you play the game? Find the expected value!

When we don't understand numbers or science at all, we end up doing stupid things. We believe in medical quacks instead of doctors, because we don't see clinical trials as important... it's easy for a quack to claim that the person he healed is proof that the cure works! And if the person isn't healed, it's because the guy didn't take enough of his cure! See, who needs numbers when you've got gut instinct? Or we think the world is just so crazy when two of our friends have the same birthday... it must be fate! Well how many people do you have to know for two of them to likely have the same birthday? This math can be done. And is done, in the book, but I won't spoil it for you.

A lot of the book is about education and the importance of good teachers, hence the quote I pulled last week about why I became an engineer. So if you're an educator, you'd probably have a whole different list of takeaways from Innumeracy. He actually argues that we should have math specialists in early education, just like kids get pulled out to go to special art and music classes, and that really made me think... why did we decide that music needs to be taught by a special "music person" but math doesn't? My fear is that it comes down to the equipment... you don't need anything as heavy as a piano to teach math, so we figure it doesn't take anyone special. That's an unfortunate decision. But I'm not a teacher.

I appreciated it as a laundry list of reasons why math is important. It does pain me a great deal when I things said to kids like "Of course you have to learn math, someday you'll have to balance a checkbook"... I think math is an artistic, beautiful thing. Appreciating numbers doesn't make you cold or mechanical or computer-like, it gets you to a higher level of thinking about the world. And it is NOT THAT HARD. We need to get past the idea that there are "math people" and "non-math people", and we need to stop laughing it off when someone says they just hate math.

Great book, important book, published in 1990 but surprisingly (or sadly) the issues in society he talks about seem strangely similar to the ones we face today.

This quote in "Innumeracy" by John Allen Paulos COMPLETELY sums up why I became an engineer!

"I remember thinking of mathematics as a kind of omnipotent protector. You could prove things to people and they would have to believe you whether they liked you or not."

Two sentences!

My whole story: I was in high school honors English class and we were supposed to write papers on Shakespeare's Macbeth. I got a D on my paper. The teacher said I didn't cite enough outside sources to back up my viewpoint, which was that Lady Macbeth's criminal behavior was caused by her life in an oppressive society that didn't offer women any means for achievement. I had some sources. But remember this was in, like, 1996... do to research we had to go to these things called libraries and use books, and search in electronic databases if we were lucky. Resources were limited, especially for a somewhat unconventional thesis.

Our teacher had given a boy named Travis an A. She said Travis' paper was extraordinary. His theme was "ambition". Every day in class, we'd talked about ambition, she'd assigned a number of critical literary essays on "ambition" throughout the lessons. There wasn't a single idea in Travis' model paper that hadn't been spoon-fed to him by our teacher. And that, she held up, was what she wanted. I'd quoted from the papers she'd given us, in addition to some of my own that I'd found, I used quotes to back up my conclusion. But it was my conclusion and she didn't like that. Drawing a logical parallel wasn't worth anything without an accomplished scholar agreeing with me, she said.

I should thank her now, because after that paper I decided the literary world was bullshit... at the same time I was taking physics and geometry, and those teachers appreciated independent reasoning. "You can't think too much," a math teacher told me. At the end of anything I did there was an answer, plain and black and white. If I proved something logically, someone who wanted to disprove it would also have to use logic... not "you don't have enough degrees".

So I never took another honors or AP English class again. They weren't important for me to be an engineer. The rest of high school I cruised through the normal English classes where they were reading popular books and learning what a verb was (I kid you not, the divides in our educational system are amazing).

Engineering turned out to be very good for me. I'm not just speaking financially. I really lucked out and love what I do.

It didn't totally save me from the "it's who you know"-ness of the world, I have been sad to find out that even the best idea ever still need a publicist and a good powerpoint that the higher-ups can understand. Dang it! But it's better than the arts I think. In science we can tell when an idea works, and we can run a test and see if a thing passes. That's why I don't think I could operate in any other field. Underneath it all, we have our numbers and that's the most important thing.

1) Tear a very small hole in the bag of M&Ms
2) Pour out two M&Ms.
3) If they're the same color, put the bag away. You only get to eat those two, until you really can't stand it and get the bag back out.
4) If they're different colors, continue taking out M&Ms one at a time until you get a color that you've already had.  Then put the bag away and eat whatever you won.

This has something to do with geometric distribution, but I can't explain it all, I've forgotten most of what little I absorbed in probability. Also, I'm too focused on the chocolate.

Several of you may remember that towards the end of my pregnancy, I got really interested in statistics of due date accuracy and human gestation. I researched, made tables, got mad at data... and finally launched my own online survey to ask women who'd had babies when they had them. And then JUST when the data was getting interesting I went and had a baby and couldn't really look at the results. But the survey didn't die, and I've been meaning to post a sort of epilogue about what I found.

The short story: that "40 weeks" idea is a pretty damn good guess at the average. I mean seriously. When I looked at just the 141 spontaneous deliveries after 37 weeks ("term"), both the mean and median date fell right smack on 280 days, or 40 weeks 0 days. This means a woman is equally likely to have her baby before the date than after it. And the most common days to have a baby are all clustered around that date, which lends to the theory that we can apply a normal curve to this (I love normal curves).

But I'd like to explore all this a lot more, not just my statistics but my reasons for the survey and answers to frequent questions/criticisms. Let's go for a ride, shall we?

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my pregnancy continues to reach new heights of nerd quality. I'd already created a due date calculator script that keeps track of what week I'm at, but now that I've been seeing it for enough weeks I added some code to tell me whether I'm actually going to have the baby on any given day:

Odds that you've had this baby yet: 3.8%
Odds that you will have this baby today: 0.9%
Odds that you'll have had this baby, three days from now: 7.4%
Odds that you'll have had this baby, five days from now: 11.1%

Oh and there's more! Here is the probability that I will have had the baby on any given day... the red mark is where I'm at now:


You call it sick, I call it beautiful.

I did have some trouble finding statistics to apply to the normal distribution. There seems to be some good agreement that the spontaneous arrival of a baby is normally distributed around these "due dates", but the deviation is different depending on where you look. I finally went with Wikipedia's statement that half of all babies are born within a week of their due date, but less than 5% are due on the due date, used a standard deviation of 9 days, and called it good.

The whole thing is insane, but it makes me feel better for several reasons:
1) I am doing the right thing by not feeling all OHMIGOD IT COULD COME ANY SECOND... my odds of having the baby now are slim.

2) Being "overdue" is not some magic instant thing. If I am three days past my due date, I'm still riding the top of that normal curve. My odds of going into labor on my due date are strikingly close to my odds of going into labor the day after my due date, or two days before. There are lots of "good odds" days besides that one.

3) I have a percentage to use when responding to any people who tell me I look "about ready to pop".

I do need to brush up on my statistics skills... although I remember normal distribution and how it basically works, my probability is rough. I mean, I have a 2.4% chance of going into labor on June 1st, but what is the chance that I go into labor on that day given the fact that I did not go into labor on any previous days? I forget how it all relates to the cumulative function (which tells me that there's a 13.3% chance that I'll have the baby before June even gets here, using area under the curve before that date). I never felt really strong at statistics... I sort of figured that if it was important, my spreadsheet would do it for me. And so far that's true! It does normal distribution... that's how I got the cumulative numbers and put them in a table for PHP to handle (PHP is smart, but it doesn't do calculus).

Anyway I'm here, I'm healthy, I'm happy, I'm armed with scripts and spreadsheets. So goes the pregnancy.

I was walking by someone's desk at work and this cartoon was hung up:



I hate to say it but no matter how many times I see that it WILL make me laugh! There's absolutely nothing wrong with that joke, it's perfect. It will always be funny. It will never get old.

Which brings me on to other perfect jokes... my man claims that the best joke in the world is this one, which I told him, after I heard it from my uncle Jim:

Q: Why does a flamingo stand on one leg?
A: Because if he lifts it up he'd fall down

And my sister once told me this one, which we never get tired of retelling:

Q: What do gay horses eat?
A: Haaaay!

And finally there's my favorite 2009 joke:

Q: What did the earth say after the earthquake?
A: Sorry, my fault

And my favorite aviation joke!

Airspeed, altitude, or brains: you need at least two.

But NONE are as important and wonderful as the cartoon that says "find X" with the line saying "here it is". I just want everyone to know that.

I have this belief that people tend to live up OR down to expectations. You tell a guy he's stupid, he's going to think school and education are out of reach and he's going to quit trying, and eventually he will be stupid. am I right?

The problem is, I think our whole nation is doing that to ourselves when it comes to math. It's so normal and socially acceptable to announce that you suck at math, that if you try to say anything else there's this uncomfortable silence in the room and people back away. Frequently I tell people I'm an engineer and instead of them saying, "That sounds like an interesting job, what do you enjoy about it?" they just say "Wow you're smart" (not in a complimentary way, in a "Wow you're a freak" way) and the discourse ends.

So we tell ourselves we're supposed to be bad at math, and we get bad at math, and then we get worse, and it's this big viscous cycle. Personally I don't even understand how you can hate ALL math, that's like hating all bread. There are so many different kinds it's really unfair to make up your mind in the third grade when you fail a multiplication test that you hate math. I wasn't great at arithmetic, m'kay, but geometry was a whole new world. it clicked. calculus was an even better one. and my relative slowness at doing multiplication in my head didn't make a bit of difference in calculus. It was about keeping an open mind and realizing that somewhere in this very diverse field there was a nitch for me.

I wonder what it's like in India, where they're cranking out engineers like it's nobody's business? I get the feeling that if you stood in a group there and said, "I hate math!" they'd all just shrug and say "Sucks to be you."