Author: bobg
What Carl Sagan means to me
Sagan’s famous Tonight Show appearances happened right around the time I was old enough to stay up and see them. Early on I remember being annoyed by his criticisms of Star Wars (to wit: that spaceships don’t make whooshing noises in space, that Chewbacca deserved a medal at the end too, etc). But then my mom, who I think had a bit of a crush on him, urged me to read Broca’s Brain, and I was hooked on his brand of science education.
Then came Cosmos, which was eagerly anticipated in our household. We counted down to its premiere for weeks. When it finally aired, the cheesy new-age music and Sagan’s, er, limited acting abilities — the camera lingered forever on what was supposed to be his awestruck face as he sailed through the universe in his kinda lame “ship of the imagination” — left us at first unenthused. But then came his story of Eratosthenes and I got another one of those emotional learning moments that I wrote about yesterday. The following is from Cosmos, the companion book to the PBS series:
[Eratosthenes] was the director of the great library of Alexandria, where one day he read in a papyrus book that in the southern frontier outpost of Syene, near the first cataract of the Nile, at noon on June 21 vertical sticks cast no shadows. On the summer solstice, the longest day of the year, as the hours crept toward midday, the shadows of temple columns grew shorter. At noon, they were gone. A reflection of the Sun could be seen in the water at the bottom of a deep well. The Sun was directly overhead. […]
Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a pronounced shadow. […]
The only possible answer, he saw, was that the surface of the Earth is curved. Not only that: the greater the curvature, the greater the difference in shadow lengths. […] For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about seven degrees along the circumference of the Earth [which] is something like one-fiftieth of three hundred and sixty degrees, the full circumference of the Earth. Eratosthenes knew that the distance between Alexandria and Syene was approximately 800 kilometers, because he hired a man to pace it out. Eight hundred kilometers times 50 is 40,000 kilometers: so that must be the circumference of the Earth.
This is the right answer. Eratosthenes’ only tools were sticks, eyes, feet, and brains, plus a taste for experiment. With them he deduced the circumference of the Earth with an error of only a few percent […] He was the first person accurately to measure the size of a planet.
In the TV show, when Sagan said matter-of-factly, “This is the right answer,” I got a lump in my throat. At once I was propelled farther down the paths of learning, teaching, science, and, of course, Carl Sagan fanhood.
It is more than just a shame that Sagan died before his time of a rare disease, ten years ago today. (This blog post is participating in a Carl Sagan “blog-a-thon” to commemorate the occasion.) There is no doubt that if he were alive today, he would never have permitted science to be debased by politics to the extent that it has in recent years. Sagan knew that we ignore science at our peril and excelled at conveying that message. He saved the world once before, by popularizing the nuclear winter theory of the aftermath of even small nuclear wars, assuring those insane enough to consider such wars that they could never avoid spelling their own doom as well as their enemy’s. Who will take up his mantle and bring the Promethean fire of science back to light a world darkened by his absence?
e to the i pi plus one equals zero
Throughout the year we covered topics in trigonometry, complex numbers, transcendentals, and logarithms. Little did we know that Mr. Arrigo was working up to a unification of all four.
One day in class he was particularly animated. We had been discussing the Euler formula, which gives this equivalence:
cosθ + isinθ = eiθ
(Here, e is the natural logarithm constant ≅ 2.718 and i is the imaginary number √−1.) He then asked us to work out the special case where θ is π (the ratio of a circle’s circumference to its diameter ≅ 3.14159). The cosine of π is −1 and the sine of π is 0, so Euler’s formula gives this amazing relation:
eiπ = −1
or, stated just a bit differently,
eiπ + 1 = 0
When Mr. Arrigo derived this result on the blackboard, he literally jumped up and down as he exclaimed, “One simple equation relating the five most important constants in all of mathematics!”
His excitement was infectious. Of course the result above is breathtaking. (If you’re not mathematically inclined, you’ll just have to take my word for it. Imagine being a world traveler collecting random antique curios from cities around the globe — then discovering one day that five of your favorite ones just happen to fit together perfectly to make an exquisite and accurate pocket watch. It’s kind of like that.) But Mr. Arrigo’s passionate presentation made it something more — an emotional highlight of my academic career.
A few years later, in college, I shared an office with my engineering friend Steve. One afternoon his actress girlfriend Amy stopped by and, one way or another, the conversation turned to mathematics. Taking turns scribbling on the whiteboard, Steve and I explained to a willing Amy how it’s possible to derive all the familiar rules of numbers and arithmetic from a tiny kernel of laws called Peano’s postulates. Amy seemed interested, so we pressed on into other topics such as geometry and its cognates, trigonometry and set theory. Thrilled that her interest didn’t flag, I mustered Mr. Arrigo’s passion and derived for her the amazing relationship between e, i, π, 1, and 0.
Soon after that, Amy’s drama-major mind finally had as much math as it could handle and our memorable pedagogical session petered out. But I could have kept going all day. I suspect Mr. Arrigo planted in me the desire to teach. I think Jonah and Archer are getting the benefit today of Mr. Arrigo’s passion way back then, and who knows? I may yet heed the urging of friends and family and become a teacher myself some day.
Mucoshave update
His beard grew bigger
He looked like a beggar
He couldn’t bag ‘er
For want of a booger
Mucoshave
(Bat|Super)man Returns
Thanks to Netflix, I saw Superman Returns a few days ago. (It was pretty good, but I had some problems with it. Maybe in another blog post.) In the story, Superman has been absent from Earth for some years; the “Returns” in the title refers to the fact that he’s back.
This made me think of 1992’s Batman Returns. What “returns” in that movie? Nothing; Batman hasn’t been away since the events in 1989’s Batman. On the contrary, in that title, “Returns” refers to the fact that it’s been three years for the audience since the last Batman movie. Batman “returns” to moviegoers. (Or perhaps, more cynically, Batman provides “returns” on the studio’s investment. Hard to be too cynical about the studio [Warner Brothers] and the franchise that famously required director Joel Schumacher to make Batman & Robin “more toyetic.”)
It’s an annoying case of breaking the fourth wall with the film’s title — a trend begun, ironically, with 1978’s Superman: The Movie, closely followed by Star Trek: The Motion Picture in 1979. Hey — we know they’re movies. (Or, excuse me, motion pictures, as the case may be.) Tell me what happens in the movie. Fight Club, 12 Angry Men, Run Lola Run, those are movie titles. In a movie called Superman: The Movie, I’d expect to see Superman busting film-industry crooks on a studio backlot in Tinseltown.
The Batman and Star Trek franchises continued offending with Batman Forever (which can be interpreted no other way than as the producers thumping their chests in an “I’m king of the world!” moment) and Star Trek: The Next Generation (“next” after what? after the last time you folks watched a Star Trek TV show, that’s what). I’ve always found it strange that none of the gatekeepers of pop culture ever raised aesthetic objections to badly chosen titles like these (until now, of course, if we can agree to call me “gatekeeper”), whose conflation of the real and imaginary threatens to take the viewer out of the fictional world even before they step in.
I was pleased to see that the [Superhero] Returns title template has been redeemed by having “Returns” refer to events in the story. Maybe now we can work on redeeming …The Next Generation by having the story be about the actual children of characters from a prior story. Ugh, maybe not.
The armory
We did not encourage swords in our house, I swear. (Nor did we enhance their allure by making a big deal out of prohibiting them.) But then Jonah won a plastic katana at the Marin County Fair (really, he did, all on his own, by popping balloons with thrown darts), so then of course Archer had to have one too. One thing led to another and… well, now look.
Yes, every object in that picture is used as a sword (and plenty of others, ad hoc), even the ones that don’t look like swords.
Every time we go to the supermarket (which is near the toy store), it’s:
Jonah: Can we go to the toy store?
Me: What do you want to get?
Jonah: Swords. [Archer nods vigorously in agreement.]
Me: [exasperated] Don’t you have enough swords?!
Jonah: Just one more. Pleeeeeease?
Well, at least the “just one more Thomas the Tank Engine train, pleeeeeease” phase is over. Maybe this one will end too. Meanwhile, guess what Archer’s Christmas wish list was? In its entirety, quote:
One little sword.
Not me
When a Terminator comes from the future looking for me (so that in the post-apocalyptic future I won’t write the Emacs hack that defeats the robot AI), this is the guy he may mistakenly blow away first: veteran yoga instructor Bob Glickstein of Maryland.
(Photo credit: Patrick Farrell.)
What brings you here?
Herewith, a selection of search-engine queries that resulted in hits on this blog, according to my server logs.
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Jonah 1, parental instruction 0
Jonah has learned to ride a two-wheel bicycle entirely on his own! And here I was looking forward to teaching him using a novel (to me) technique suggested by my friend Bart.
When I learned to ride a bike, it was after hours and hours, spread acrosss days and days, of coaching from my dad, who jogged along behind me holding my bike upright, like a human pair of training wheels. One day as I was finally getting the feel of it, I asked him a question and got no reply. I turned around to see him receding into the distance. He had let go, and I was riding the bike on my own! In a panic I literally leaped off the bike onto concrete, setting back my bike-riding efforts by a few more days.
I remember my dad’s help with great fondness, but Bart’s method made much more sense when he described it to me. The student straddles the top bar of the bike, feet flat on the ground, hands on the handlebars, and walks the bike around for five minutes to get a feel for it. The student then stands on one pedal while kicking off the ground with the other foot, like riding a scooter. After ten or fifteen minutes of that, the student is ready to get both feet off the ground and start pedaling.
But Jonah’s gone and learned to ride on his own initiative, using the small learning bikes that his preschool has in its schoolyard. I am proud! …but just a little disappointed. That’ll pass, though, come springtime, when we light out for the park and ride together!
Last Lost
I have been catching up on season two of Lost courtesy of Netflix (since I no longer have cable). When I added season two to my Netflix queue it amounted to seven discs’ worth of episodes. As I finished each one I eagerly looked forward to the arrival of the next. Most episodes in season two ended with a “HOLY CRAP” cliffhanger.
I finished disc six just last night and HOLY CRAP! I got it in the mail to Netflix first thing this morning hoping for disc seven to arrive by Wednesday. I logged in to Netflix to see the episode titles on the next disc… and discovered that disc seven is merely the “special features” disc with no new episodes on it. I finished season two without even realizing it, and now I can’t see season three until it comes out on DVD. Bogus!