4 Days to Tau Day 2011: Tau and Its Digits « Not About Apples

24 June 2011

Today on Not About Apples, I celebrate the approach of Tau Day with an image of Tau constructed from its digits.

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Or just grab the image: Tau Digits


5 Days to Tau Day 2011: why use radians? « Not About Apples

23 June 2011




Today on Not About Apples, why mathematicians prefer radians to degrees, and what that has to do with Tau Day.  Also, I use the word “myriograde”.

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Star Wars Nerds, Why I’m Not One, and John Hodgman

23 June 2011

I’m currently playing my way through “Lego Star Wars: The Complete Saga”, which I got for Christmas last year.  It’s my third Lego experience, after Lego Batman and Lego Harry Potter, and the Lego magic is still very much alive for me.  Those games have such a high fun factor, you really feel that you are not just gaming but playing.  And play is sacred.

I say “the Lego magic” and not “the Star Wars magic”, because I really am playing it chiefly because it’s a Lego game.  I know that there are people, hordes of them, who might pick it up because of their love for Star Wars.  But not me.  I’m a nerd for many things but not for Star Wars.  I bear Star Wars cultists no ill will, and indeed I have a little envy.  I wish I loved those movies the way they do.  And I like the original trilogy just fine.  But I don’t love it.  And I never will.

Because the first Star Wars movie I say was Phantom Menace.  Enough said, I guess.

I never watched the originals as a child, even when my friends were talking about them.  I didn’t watch a lot of movies.  They were on my to-watch list, but it never happened.  When I heard about the prequel trilogy, I was excited.  I planned to watch the six movies in story order.  Episodes I through III as they came out, and then the next day an original trilogy marathon.  That’s not how it worked out, though.  After the first movie I was sufficiently disappointed and nonplussed that I rented the originals all in one go, wanting to see what it was that had made so many people so excited to see .. that.  But by then it was too late for me.  It’s true what they say about first impressions.

Last weekend, the Not My Job segment on “Wait Wait Don’t Tell Me” was quite apropos: Simon Pegg, actor and author of Nerd Do Well.  (You can read or listen here.)  Peter Sagal and Simon Pegg spend a good bit of the conversation nerding out about the original Star Wars Trilogy (stirring in me, as always, a quiet jealousy for the love some people have for those movies), and the conversation takes an angrier turn when they come to discuss the prequel trilogy.

This reminded me of one of my all-time favorite pieces from This American Life: John Hodgman’s “Jar Jar Head”.  It’s Act 3 of this episode.  If you don’t know this about me already, I’m an unapologetic Hodgmaniac.  I read and reread Areas of My Expertise and More Information than You Require, I watch and rewatch his You’re Welcome clips on The Daily Show (too hard to pick a favorite clip, but my favorite line is surely “No, if anything, it’s not.” from this one; surely one of the all-time great throwaway lines).  But this is different.  This is John Hodgman before his persona was established, before he was playing the character John Hodgman.  The emotion is real, the poignancy and vulnerability are not feigned.  That’s right, it’s vintage John Hodgman.  Please, take 10 minutes and listen.

6 days to Tau Day « Not About Apples

22 June 2011

Back after a long hiatus on Not About Apples, where I’m kicking off my countdown to Tau Day 2011 (which is next Tuesday) in true Cap-style, by digressing about exponential functions. Some links to what Tau Day is all about, and a fuzzy place between subjectivity and objectivity.

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Taking my daughter to Cedar Point

21 June 2011

I’m sitting here at my computer desk in Fenton, MI, and as I sit here looking back on the last seven hours of one of those days where working really feels like working (a lot of particularly tedious technical writing and some wrangling of Sage and Mathematica), it’s almost hard to believe that, exactly one week ago, I was riding Thunder Canyon for the seventh or eighth time with my daughter, dripping with icy water and mentally going over the symptoms of mild, moderate, and severe hypothermia.

(Note: Though I am posting this entry at about midnight, I actually wrote this post at 3 pm.  Please, nobody get the idea that I was sitting with my 8-year old in icy water in the middle of the night, after the park was already closed.)

It was  a special father-daughter trip, no brothers allowed, to celebrate the end of first grade.  Now that she has a two-year-old brother and a two-month-old brother (and that ticks over to three months in two days), my daughter and oldest child doesn’t get as much attention as she used to, and her life is, like her parents’, to some extent ruled by the whims of an infant and a toddler.  We wanted the beginning of her summer to be memorable and fun and all about her.  A whole day of just the two of us at America’s Roller Coast, a place I visited more or less yearly in my own childhood but she had never visited, seemed like “just the ticket”, as I might say if, instead of blogging this at you, I were sipping brandy and wearing a smoking jacket while discussing the trip with you in your parlour.

So the night before, we told her to pack up her bag for a trip with dad and my wife helped her pick out an outfit and a spare, etc.  We were gone by 6:15.

Digression that “just doesn’t matter; it just doesn’t matter; it just doesn’t matter”: In my own childhood, the official start-of-summer commemoration was the ceremonial watching of Meatballs with Bill Murray, especially for my sister.  Chants of “it just doesn’t matter”, or references to “Wudy the Wabbit” are pretty much guaranteed to be well-received in my family.  I did suggest to my daughter that she could have a tradition-movie like that, tried to explain how much her favorite aunt had enjoyed doing so.  She smiled and said she wanted to, but mostly she looked puzzled.  I guess, with the amount of television and movies she watches on a daily basis, the idea of getting excited by a movie every year has hard to make sense of.

I beat all the heavy traffic, and we got to Cedar Point before they officially opened.  There is a gate that opens at the official start time, and by the time it opens there are dozens and dozens of rows of people pressed against the gate.  We were in the first row, right against the gate.  I could tell that my daughter felt like one of the cool kids, getting to be one of the very first in.  When the gate opened, we headed to the back of the park and worked our way forward (that’s the trick, friends).  We started with the Maverick, an excellent ride that I’d never been on, because my daughter said she was brave and tough and all.  Apparently that drained all the fight from her, though, because after that she only wanted kiddie rides and the Scrambler, Tilt-a-Whirl, Matterhorn type things.  Nothing with a roller coaster track, nothing with screaming, nothing with upside-down.

You might think that that would ruin a day at Cedar Point, but it worked out just fine.  There are more kiddie activities than I remember from my youth.  She made many friends at Camp Snoopy and Planet Snoopy.  We saw an amusing ice skating show.  She indulged my love of the paddleboat excursion.  And we spent hours at the water rides.  We bought ice cream and french fries and all the must-eats, and I had brought a bag full of sandwiches and tacos and snacks of all kinds.

We had more time to talk, and she had more interest in talking, than had been the case for a very, very long time.

Digression that makes mouths happy: When my family went to Cedar Point each summer, my mom would always bring a giant bag with all the sunscreen and bug spray and waiting-in-line candy ‘n snacks.  You may never have thought about this, but you have to make candy selections with a certain amount of care when you’re packing for a full day of standing around in the hot sun.  Melting is a problem.  The preferred candy: Twizzlers.  Sometimes Werther’s, sometimes other things, but always Twizzlers.  As I planned out the trip in my mind, the first thing I knew for sure is that I would be packing Twizzlers.  To this day, that weird waxy strawberry flavor just tastes like ride queues, summer, and childhood.

Lately I’ve been feeling unstuck in time.  Not the full-on Billy Pilgrim, and no Tralfamadorians, but unstuck in my mind.  I’m 30.  I can’t process how quickly my children are growing up.  Having a new baby boy puts in sharp relief how much my toddler boy has grown, but also makes me feel as though it were just last week he were a baby.  More and more often I’m dreaming that I’m talking to my children, all grown up.  My daughter is 8, but sometimes she acts older, sometimes much younger.  Under those circumstances, it was questionable planning to visit a place where I have so many childhood memories.  I spent a lot of the day flashing back and forth between what was happening and memories of the same places when I was a kid.  Back before it was Peanuts.  Back when it was Berenstain Bears.

Digression that never will kick that football: I was not expecting my daughter to be so enamored with the Peanuts stuff.  I had no idea that she knew the characters.  I was taken even more by surprise by how much of a hold Peanuts still has over me.  I read it as a child, of course (who didn’t?), and hadn’t really thought about it for quite a while, so I didn’t know how deeply embedded in my psyche those characters were.  The power is Schulz’s simplicity, the understatedness.  Who can’t relate to lovable loser Charlie Brown?  Who doesn’t have a Lucy and a Linus in their life?  And, when you take one of life’s twists and turns a little too fast, is there anything better to say than “Good grief!”?

Meta-digression. Speaking of the passage of time and things that are timeless, speaking of things that put in sharp relief that I am getting older, speaking of all-time wonderful comic strips. have you seen Hobbes and Bacon on Pants are Overrated?  The best commentary I’ve read is here, by Robert Krulwich.  Let me just say that they are toying with powerful forces.

My daughter is typically in bed well before 10 pm, so it was far from a foregone conclusion that we’d be able to stay the whole day.  But she got her second wind, and then a third and a fourth, and she was very much awake when we sat down just in time for the fireworks and laser light show.  I told her how much I loved her, how glad I was to have her as a daughter, how much I enjoyed spending this special day with her.  She told me I was the best dad and then we watched the show.  An American Portrait, it was called, and it was patriotism to the max.  It was pretty good, actually, but I confess that I miss the rock-and-roll-themed laser-light show from my childhood.  Every time I hear “What I Like About You” by the Cars, even today, I am teleported back into my own childhood, and it’s dark and I have spent a whole day roller-coastering, and I’m about to fall asleep in the car and roller-coaster in my dreams.

This time, of course, it was my daughter who fell asleep about three minutes into the return car trip.  I didn’t have that luxury.  My three-ish hour drive home was brought to you by three cans of cherry Nos (or, as I like to call it, the Drink of Ultimate Desperation).  I got home after 1 am, more tired than I’d been in quite a while, but also filled with that vague but satisfying feeling of having done something.

I don’t know exactly what I wanted or expected from the experience, and I don’t know what I got from it.  I know that I wanted it to be .. meaningful, and I think it was, but what exactly it meant .. to me or to her .. I couldn’t really say.  I have a slightly better-defined notion of what I hoped my daughter would get out of it, and though she talks happily about how much fun she had, you never really know what’s going on in someone else’s head.  Not ever, really.  Not even your best friend or your spouse.  Not even your child.

Not even yourself.

Euvoluntary Exchange and the “Closer to Perfection” Fallacy

21 June 2011

The most recent episode of EconTalk features fan-favorite guest Mike Munger of Duke University.  His goal here is ambitious: to “build a bridge between philosophers and economists”.  The question: why is it that some types of voluntary transactions are seen as repugnant and made illegal, even though all parties to the transaction are made better off and enter into the transaction voluntarily?  The question (a special case, at least) is also asked another way: Why does it happen that it is legal to provide certain goods or services, but not to charge what they are worth?  Examples include organ sales, blackmail, “price-gouging”, and various aspects of low-cost labor.  (I should point out that Prof. Munger does not claim here to establish what the laws “should be”, just to better understand the reasons for some laws and social norms that seem counterproductive from an economist’s standpoint, and why they persist despite undesirable unintended consequences.)

Also, some insight into German beer festivals.

(If you’ve never listened to EconTalk before, you might want to check out some of Mike Munger’s previous appearances on EconTalk first.  If you’re already listening to the current episode and liking it, you’ll surely want to hear more from him.)

Now, the key ingredient in his analysis here is something called BATNA (best alternative to a negotiated agreement), which is used here as a way of economically quantifying imbalances of power.  (Overly simplified and blatant example: If you are lost in a vast desert and I drive up in my desertmobile, offering to sell you water.  My best alternative to selling you water is to drive away and sell it somewhere else.  Your best alternative may very well be to drop dead.  Consequently I can charge you very high amounts of money, and we’re both better off than if we had made no deal, but there is something repugnant about my behavior.)  He’s probably on to something, but the conversation left me thinking about something rather different.

There is a very common fallacy in human thinking about rules and making rules, about how our views of morality and our preferences inform our lawmaking decisions.  At least, I think it’s common, if not pervasive.  It’s not one that I have seen on the “standard” lists of fallacies (such as this one), so let’s call it “Closer to Perfection” fallacy.  (Those of you who like your fallacies and rhetorical terminology in Latin, knock yourselves out.)

Closer to Perfection Fallacy.  If a certain phenomenon would not occur in an “ideal” world, making that phenomenon illegal or impossible can only make the world more like the ideal.

Example. In an ideal world, people with water would seek out people lost in the desert to give them water free of charge, out of mercy, and there would be no need for you to buy my water for $1000.  Consequently, it should be illegal for me to sell it to you.

I believe that many of us are prone to make this mistake, and that it says a lot about why genuine and well-meaning people can do so much damage when attempting to legislate morality.  What do you think?  Does this, or something like it, already have a name?



4 November 2010

The physicist Wolfgang Pauli (the “Pauli” of “Pauli exclusion” and “Pauli spin” was, so the story goes, fond of dismissing half-formed ideas and half-baked articles which he was reviewing for publication by saying, “That’s not right.  It’s not even wrong.”  It was the harshest criticism he could give.

I am currently teaching a math course intended for future teachers, and I recently began a class with that quote from Pauli.  In the context of physics, “not even wrong” meant that a paper, idea, or theory did not lead to any predictions that could be tested (is not “falsifiable”, an essential criterion for a scientific idea).  However, “not even wrong” applies outside physics and science to those ideas that are so poorly articulated, so barely-formed, that there’s no meaningful way to respond to them.  Every teacher, I reminded my class, will all too often find herself talking to a complaining student appealing for more points on a homework or an exam, demanding “Why is this wrong?”

If the teacher is lucky, there is an answer to that question.  “It actually happened in 1965, not 1978.”, for example, or “You said ‘rhombus’; you probably meant ‘rectangle’.”  A specific error of fact or reasoning that can be identified, corrected, responded to.  Usually, though, that’s not the case; instead, the answer on the page is a word salad, some vocabulary from the course strewn haphazardly on the page in the hopes of some partial credit or lucking into the right answer.  If the class is a math class, it may not even be a sentence or recognizable as English.  And what’s so frustrating for the teacher in this scene is, there’s nothing to point to!  There’s no particular wrong word or error in reasoning.  What the student has done is not even wrong.

A few years ago, I got fed up with this situation arising while I was grading.  I decided that, while I was happy to write extensive comments to explain mistakes, I had no intention of spending that kind of energy on someone who hadn’t bothered to make any sense.  I started writing “intrangible” on such passages, on the idea that marking them with actual English words gave them too much credit.

I have heard that at least one former student of mine has done some teaching of his own, and uses the word “intrangible” in his own lectures and grading.  How about that.

More touching actually was when I received a visit from a different former student.  She had struggled mightily in my class, and had not found much success at that time.  However, subsequent to my class, she had taken an interest in more sophisticated mathematics, and had managed to teach herself quite a lot.  After exchanging pleasantries, she asked me a question that she had been thinking about.  The question was complex, and subtle, and I had to think for several minutes before I could answer it.  Indeed I was proud of her!  But as I was thinking, she got nervous, and asked tentatively, “Oh dear… was that intrangible?”

I assured her it was the most trangible thing anyone had said to me all day.


Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law is also the name of an excellent book (ISBN: 9780465092756) by Peter Woit on string theory for a wide audience.  If you want a friendly introduction in layman’s terms to string theory and why it is and isn’t important, I recommend it.  If you don’t have the time or attention span for a book, this xkcd comic makes essentially the same point in a second or two.


When a student says to me “Why is that wrong?” with that challenge in his voice, of course the temptation is to counter-challenge “Why would you think that it’s right?” (Or “Why would you think that’s a sentence?”, if I’m at my most exasperated with what some student think passes for acceptable writing skills in math class.)  Sadly, a teacher is so often prevented by etiquette from saying what would be the most apt thing.  (Another thing I wish I could say sometimes, when a student comes to my office demanding help with a homework problem, having admitted or demonstrated that he hasn’t really thought about it yet, or sometimes hasn’t even read the whole thing, is “Have you tried trying? Often that helps.”)