NAA: Bhargava’s Factorials

New post at Not About Apples.

Not About Apples is back with a vengeance.  Today, Bhargava’s generalized factorials, a relatively recent gem of mathematics (discovered in our lifetime) gleaned from the Joint Math Meetings in January.  Who’d have thought there was more to say about ? It’s a little weightier than some of my posts, but I think it’s one of the most worth-the-effort.

Permalink: Bhargava’s Factorials.

NAA Link: Math Mutation Podcast

I recently discovered the Math Mutation podcast, which might be of interest to many of you.

According to the tagline, Math Mutation explores fun, interesting, or just plain weird corners of mathematics that you probably didn’t hear in school.

At the time of my writing this, there are 120 episodes, but don’t be intimidated.  Each is only a couple minutes long, lasting just long enough for the host to show you a little gem of mathematics or mathematical thinking.

In such a short format, a certain amount of oversimplification is inevitable, and much that is fascinating gets left unsaid.  But the amount he manages to say in such a short time is commendable, and it’s always enough to get you thinking.

Better, each episode comes with some useful links, so if something grabs your attention you’ll have some leads on where to get more information. Even if the links aren’t enough, the podcast reliably gives you enough information to successfully google for more.

So if you want to see the weirder side of math in a user-friendly setting aimed an extremely wide spectrum, and you like your ideas in bite-size portions, help yourself to a Mutation or two.

Daddy-Daughter Dance

The highlight of this weekend for me was yesterday evening, when my daughter (6 years) and I got all dressed up and went to the annual Daddy-Daughter Dance.

It’s an activity run by the local PTO, and I hear that it sells out every year. They decorate one of the middle school gyms with pink balloons and Valentine’s Day stuff, get a DJ and those colored light balls that make me think of roller skating night when I was a kid, some hors d’oeuvres and punch, the whole bit. The idea (beyond fundraising), I think, is to give all the girls an experience of being taken on an evening out by someone who genuinely loves and respects them. It’s really a sweet thing.

I’m glad this is a part of my fatherhood experience, though it’s not really something I was expecting; certainly it doesn’t jog with any memory of my own childhood. Mother-Son Dances, not so popular. I remember one or two Mother-Son miniature golf afternoons in high school, and if I stay in Fenton Gabriel and Susie will have Mother-Son Bowling to look forward to, but it’s not the same.

I cherish any chance like this, to spend quality time with my daughter that doesn’t just degenerate into her running around or screaming. They grow up so fast. I remember the first time I held Datura as a baby, how tiny she was. Now she’s almost seven and growing like a weed. She’ll be taller than me before I know it. Some experiences mess with your head that way, they make you think about the past and the future and how quickly it all goes by. There was a moment in my wedding reception that I think about often — Susie and her father were doing the father-daughter dance, and as I was standing there, I noticed that Datura was sitting next to me, looking back and forth between the dancers and me. And I realized, one of these days we’ll be doing that dance at her wedding. How long do I have? More to the point, on that day, when I look back fondly on now, how fast will it all seem to have gone by?

But I digress. Daddy-Daughter Dance. Yesterday. Good time. The PTO really puts a lot of effort into it. Even some decent coffee for the dads. I had fun, and I think Datura did too. And I learned some things.

1. There are a lot more dads around here with two or daughters than I would have expected. You could tell, because they walked in with one on each side, and because most of the paired and tripled daughters wore matching dresses.
2. Girls are graceful. Evidently they just have an inborn ability to dance that kicks in around seven or eight. Little boys don’t have that.
3. Playing the Macarena was a bad choice. The daughters are too young to know it, the dads are too old to remember it fondly. What happened is a lot of people just looking around awkwardly, and like three daddy-daughter pairs trying to be good sports.
4. They really need to find better music. Daddy’s Girl? Really? The one with the shrieky girl on the chorus about a guy coming to terms with having a daughter even though he wanted a son.
5. At least they learned one lesson since last year and didn’t play Superfreak. “She’s a very kinky girl, the kind you don’t take home to mother.” is a line that no dad should ever have to hear in the presence of his daughter, and no daughter should ever have to hear in the presence of her dad. According to the DJ, it was some dad’s request. Whoever you are, that’s messed up.
6. My daughter’s favorite song, according to her, is the Chicken Dance. Yes, they played it at the dance, but it was the second-to-last song, and it only made it in because my daughter requested it repeatedly. (To any fathers out there, yes, we are responsible for us all getting in a circle and doing the chicken dance, after the night was almost over and you thought you were safe from such things.)

By the way, yes, I did the Chicken Dance with my daughter. I also did the Hokey Pokey. Last year I did the Cha-Cha slide too (this year she was taking a food break during that one). I am willing to embarrass myself for my children, if that’s what it takes for them to have fond childhood memories with me in them. That’s worth several chicken dances, if you ask me.

Groundhog Day never works out right

Well, it’s happened again, or more like failed to happen again. Another Groundhog Day has come and gone, and, *sigh*, once again I woke up in the Third of February. I’m not going to lie, every year there’s a part of me that hopes that I’ll go to bed at the end of a Groundhog Day, and I’ll wake up the next morning and the clock will tick over to six o’clock and the radio will play “I Got You Babe”.

Hasn’t happened yet, but I keep hoping.

Those of you who haven’t seen Groundhog Day will be forgiven for being a little bit confused. On the other hand, you will *not* be forgiven for not having seen the movie. Honestly, has anyone not seen this movie? I don’t think it’s an exaggeration to call it a cult classic. On the radio yesterday, I heard a story claiming that Groundhog Day gets a lot of play as a sort of parable across a broad spectrum of religious groups.

Doesn’t surprise me. Say it with me, people, “I’m not the God, I’m a god.”

I’d love to have a few hundred attempts at the same day. There’s a stack of a couple dozen math texts that are sitting on my desk that I never manage to get to, and hundreds of non-mathematical books highlighted on my list. There are problems I know I could solve in a few hours at the whiteboard that never quite happen. I’d spend some whole instances of Groundhog Day just watching movies with my daughter, or crawling around with my son, or spending time with my wife. There are a thousands things that it kills me that I don’t have time for, and

I know that, in the movie, Groundhog Day in Punxhatawney is Bill Murray’s penance. But it sounds like paradise to me. I’ve got a good thing going here, and if I could loop one of these tracks for a while, I’d do it in a heartbeat.

Because what’s happening now is that time is just blowing by me. That’s how it seems. Wasn’t it New Year’s Eve about a week ago? And here we are four-plus weeks into the new semester — is it even the “new” semester anymore? — and the first midterm’s in a week and a half. My son’s a year old — I know I’ve said that already, but part of me keeps thinking that I’ll realize we were counting wrong and he’s really just six months. And my daughter’s three or four. And I’m twenty-two. And my little sister, who just moved into a gorgeous little apartment in San Francisco — I saw it when I was in town for the Joint Mathematical Meetings — is, I’m pretty sure, still eight years old. A couple weeks ago I drove up to Saginaw Valley State to grade the Michigan Math Prize Competition. To grade it? Really? How am I allowed to grade it? Wasn’t I competing in that one just a year or two ago? According to my calendar, which I’m less and less sure I can trust, it’s been more than a decade.

In the time it took me to type this post out, my son probably learned to juggle. It all goes by so fast.

P.S.

While we’re on the subject of vintage Bill Murray, What About Bob? anyone? Baby steps? Death therapy?

Makes my lips numb just thinking about it.

One-Year-Old Creepy Kid

Yesterday we met my parents at Great Lakes Crossing for a slightly belated celebration of my son’s first birthday.  (I had to teach last Tuesday evening, when his true birthday was, but I’m told he was taken out to dinner and given some cheesecake that he did not like at all.)  My daughter’s idea was to take my son out onto the play area (that giant fake food) for the first time.  This actually turned out to be a better plan than we could have hoped for.  In the past week and a half, he’s become an all-terrain crawler and climber.

At first he just went to the nearest fake ice cube and climbed up and down and around, in short making himself the king of the ice cube.  Eventually he explored and climbed more and more of the area, evidently having an amazing time.  What impressed me most was the little guy’s bravery.  I was concerned because there were so many much bigger kids running, jumping, and falling all over the place, but he seemed totally unfazed.  He’d crawl, pause until the stampede passed, and then keep going.  I guess when your big sister’s primary form of interaction with you is to run up to you screaming, pick you up, whirl you around, set you somewhere else, and vanish, you toughen up fast.

It really bothered me that I wasn’t going to be able to get home from Ann Arbor on Tuesday before everyone was asleep, so I took a nonstandard approach.  I decided to take him out to the Cafe Aroma (aka my Fenton office, aka my northern command center) for an hour of father-son time before running him to day care and going to work.

When I announced this plan to my wife, and again when I announced it to my sister some time later, each said something like “He’s too young for coffee!”  Give me a little credit here, I never intended to get him coffee.  He had steamed milk, with a smidgeon of vanilla.  He tried to steal my coffee until he finally actually tried his own drink and realized, apparently, that it was the drink of the gods.

He was actually a very good coffee buddy.  He sat still on my lap, drank his steamed milk, took little bites of the bagel we were sharing.  He set the mouth most full of bagel, cheeks chipmunked out and everything.  I was warned by the other patrons that I’d end up wearing that bagel, but in fact he got it all down.  He seemed to understand from the other groups of people that when people go out to coffee together, they converse, and whenever I wasn’t talking to him he’d babble at me.

The comic high point of the visit?  The oldest of the resident coffeeshop geezerettes told me that, “Well, he sure looks like a creepy kid!”  I didn’t know how to respond.  A creepy kid?  Really?  Usually he gets called “adorable” or “handsome” or (yesterday at the mall, in line at Wetzel’s Pretzels) “dangerously attractive”.  So I looked back at her, hoping for a cue for how to proceed?  Was this some form of old lady humor?  She seemed kind and smiling, not looking at me at all in the way of someone who had just insulted my firstborn son.

Then a slightly less old geezerette came to the rescue and explained that “creepy” was slang from a long time ago, that she meant “He sure looks like he loves to crawl.”

Like any parent, I think, I can’t believe that it’s been a whole year of having him already.  It’s gone by so fast.  But more than that, I’m noticing how fast he’s growing up right now, every day.  In the five days I was gone for the Joint Meetings, his development kicked into overdrive.  His first haircut’s around the corner.  His speech is coming along every day.  He plays with toys and interacts with objects in much more complicated ways.  As of the night before his birthday, he suddenly, without obvious reason, sleeps peacefully through the night after a year of keeping Susie up all night!  He has six teeth now, four on top and two below.  Yesterday around lunchtime he discovered that he likes carrots.  Around dinnertime, macaroni and cheese.

Just think how much bigger, in relative terms, his world gets every day!  There is nothing comparable in my present or future.  I can’t even imagine what he’s going through.  And going through it smiling!

As his Uncle Scott so aptly says, “he smiles relentlessly”.

The Road Not Taken

On Saturday, as I was driving to Saginaw Valley State University, I happened to hear the Writer’s Almanac with Garrison Keillor.  It was actually more interesting than average for that particular program, beginning with a discussion of <i>Roots</i>, and some interesting facts about its transition from print to film. If you’ve ever heard Writer’s Almanac, you know that Keillor always closes by reading a poem.  Usually the poem is one I’ve never read, by someone I’ve never heard of (but then, I’m really not very knowledgeable about poetry), but on Saturday it was “The Road Not Taken”.  Which could not be more familiar.

I imagine that almost everyone reading this has heard this poem; it’s the one that starts “Two roads diverged in a yellow wood / and sorry I could not travel both…” and ends “Two roads diverged in a wood, and I– / I took the one less traveled by, / And that has made all of the difference.”

Everyone’s heard this one, it’s part of the canon, and it is to my knowledge invariably taught to schoolchildren as a voice in favor of doing the nonstandard thing, of finding your own way, of notn being afraid to be different, of taking chances, etc.

It wasn’t until quite recently that I realized that that’s the wrong way to read the poem.  (I’m pretty sure the origin of this idea came to me from one of the radio shows I compulsively listen to, presumably either This American Life or RadioLab, but a cursory search didn’t identify the source.)

The thing to notice is that, in the final stanza, the speaker does not say that he chose the path less travelled.  He says that HE WILL SAY that he chose the path less travelled.  Indeed, when the narrator examines his choice, “Both that morning equally lay in leaves no step had trodden black.”  There’s nothing to base a choice on.  The only time he actually hazards that there is a discernible difference between the roads, he immediately backpedals. “Though as for that, the passing there // had worn them really about the same.”  They are essentially indistinguishable.  The author is not saying that he chose one path over the other for any great reason.  The point is not that choosing the path less travelled leads to success, indeed he’s not even saying with confidence that he’s choosing the part less travelled.  The narrator is saying that he will look back on this choice as if it were pivotal, that he will tell the story as though it were.

Don’t mistake me, I’m not criticizing the poem or the poet, far from it.  I still cherish this poem now that I understand it better, maybe more.  If anything it seems truer.  More comforting.  We go through our lives, we’re faced with a lot of choices.  Sometimes, often, there’s no good basis for a decision, but we choose.  And we go through life’s journey, and where we end up is based on our achievements and our good decisions, but at least as much on our arbitrary choices and random happenstance.  And when we look back on our lives, we make up a story.  We make up our life story looking back on it.  We decide, by how we tell the story, where the defining moments in our life were.

The importance of precision *or* Why are mathematicians so picky? « Not About Apples

New post on Not About Apples.

Mathematicians have a highly developed language for precisely dealing with ideas, and we can get awfully insistent that others share our level of nuance for even simple mathematical objects.  Your math teachers probably seemed unreasonably fussy about minor computation errors, or wording your answers in a way that was not, strictly speaking, true.  Why is that?

Permalink: The importance of precision *or* Why are mathematicians so picky?.

100 Games Cupcake Game

This will be the all-time best thing ever for today.

100 Games Cupcake Game.

Kudos to Joe of Planet 3 for bringing this to my attention.

Personally, I’m partial to Carcassonne, Munchkin, and Zork.

NAA Link: Rubik’s Hypercubes

(see this post in it’s natural habitat)

Tired of your mundane three-dimensional Rubik’s cube? Want a hands-on activity to help you make sense of the fourth dimension? Download Magic Cube 4D. The interface is really quite intuitive (and that’s saying something considering how un-intuitive the fourth dimension is).

Oh, and if you consider 4-dimensional Rubik’s Cubes too easy to be worth your time, perhaps you’d prefer Magic Cube 5D.

What To Do With 800 Pinball Machines? Play Them!

From today’s Weekend Edition Sunday on NPR… now this is a man after my own heart!

What To Do With 800 Pinball Machines? Play Them!