Calculus without Calculus

Two-thousand years before Isaac Newton was born, an unknown Greek reflects upon the world convinced there must be some order to the chaos. We imagine our hero come beard-to-beard with Aristotle's crude physics -- spurred on, we imagine, by recent tragedy: a brother's trireme lost off the coast of Attica in a storm.

Aristotle consoles. The sailor drowned because the bottom of the ocean is the natural place for him.

This vexes our hero (let us call him/her Kittycules), for s/he observes some things do not seek the bottom of the ocean. Ducks, exempli gratia. Witches. Very small rocks.

Because that, too, is their natural place, Aristotle retorts undeterred. Very tremendously natural place. Lots of people are saying that.

It cannot be denied Aristotle's physics leaves much to be desired. Talk of "things seeking their natural place" looks nice on a bumper sticker, but it don't provide a useful tool. However, what form would a useful tool assume? It would take two millennia (and a plague) for humans to work that out.

But it need not have.

Deriving Energy Quantization using Matrix-Based Quantum Mechanics

So I was home Saturday night with nothing to do because Netflix failed to come through with my Mr. Robot DVD (failed to come through again, I should say*), so I did what I always do when life hands me lemons: I drink and rant on teh blog.

* Seriously, Netflix, what the damn hell? I used to get two cycles per week. Now a turn-around takes ten business days. If you're not going to support your DVD service, then eliminate it. Don't do the typical American business thing where you screw the extant customer base with declining service until somebody shows up at your office with a Carcano. Tweeners whose mommy pays the streaming bill may snigger at us DVD players, but I would remind you we are the reason Reed Hastings is banging supermodels on a private jet.

But I digress.

How the Jacobian is like a Dead Raccoon Stuck in your Wheel Well

So me and Donny was driving down to Lino the other weekend (muskie season is fast approaching and REI was having a sale on wire leaders) when we experienced an automotive emergency that got me thinking about the Jacobian.

Donny fancies himself something of a gearhead. He spent a year in automotive cert over at the vo-tech but had to drop out after my sister got pregnant (got pregnant again, I should say. That girl is more fertile than the Nile river basin). So now he mostly does piecework around town. Snowmobiles, Snowcats -- that sort of thing. The big money is in Evinrudes, but the Lino CC got a lock on that and ain't no way they'd let a Circle Pines boy like Donny into their club.

Anyhoo, Donny's pride and joy is his '71 Chevelle, which isn't much to look at but under the hood is quite the formidable piece of machinery. Sort of what you imagine Springsteen drove over to Mary's house after she got raped at graduation.

Footnote: Holy cow. I just now realized Mary got raped at graduation. That's messed up.

Lots of stuff had gone under that hood, like solid lifters and a Holly double pumper and other words I used to know before graduate school pushed them out. Donny boasted he put 350 heads on a 305 engine, just like Patterson Hood. He, also, did not have good intentions. So he opens it up a bit, what with eight lanes of light traffic and a converging horizon, although I cannot confirm nor deny any laws were broken.

And that's when it hit us. Or, rather, we hit it.

Mick Jagger does not understand Conditional Probability

Funny, got no money.
I throw sixes and sevens and nines.

I went to engineering school with some very smart women. Case in point was a Yugoslavian prodigy doing her doctoral dissertation on nonlinear viscoplastic constitutive modeling and I'll bet some of those aren't real words. Yet, her most enigmatic quirk was not a Macedonian heritage nor a frightening alacrity with tensor calculus, but rather an unholy obsession with Mick Jagger. Yes, I mean in a vant to have his babies kind of way. And, no, I don't mean Rock n' Roll Circus Ed Sullivan prime Mick Jagger. I mean the AARP member recently seen grinding against Christina Aguilera and Martin Scorsese believed it was ethical to film the act. I haven't been this squicked out since watching Steven Tyler mack on Tal Wilkenfeld in that Jeff Beck YouTube promo.

Oh, I kid because I love. Still, I must find some way to assuage my profound embafflement, for I'm told this is not a uncommon affliction. Women of all stripes have an unholy obsession with Mick Jagger, regardless of age, color, creed, or alacrity with tensor calculus. Apparently he continues to receive sufficient underpants to build an underpants fort every day of the week and have underpants fort fights with Tom Jones. All from sisters, little and otherwise, who should know better. Meanwhile, the number of strange women offering themselves to LabKitty is quite modest, and I have a blog and everything.

It's a right mystery, one that makes a mockery of my four university degrees, adult orthodontia, and common sense. Fortunate for me, then, that Mick has questionable math skills, one heartbreaker who will forever sway beyond the reach of his sticky fingers. Thus my vessel of ego repair appears. I sing of the probability libel on display in Tumbling Dice, a song he penned circa 1972 and you don't much hear on the radio anymore because Clear Channel decided they're going to play Adele over and over until we all lay dead with chopsticks jammed in our earholes. Why be all about the variety when J. Peterman can simply assure you it is true? But I digress.

What's that? you ask. Probability libel? Kitty, whatever do you mean?

Yes, it's time for another LabKitty browlfsplainer! Read on.

The Golden Rule

I write LabKitty for myself as much as anyone (and if you've seen my analytics you know how true that is. High five!). A kind of public record of self-discovery in the spirit of Augustine's Confessions or Marcus Aurelius' Meditations, albeit unlike the latter only occasionally written while drunk (the Emperor has no prose). A tale of a small town cat coming of age in the cruel world of academics.

Mostly, however, LabKitty is about trying to undo what the hateful math faculty did to me at Circle Pines U. My Alma Mater. Not its real name of course, as if I need point that out. The only thing university administrators love more than indirects is a good libel suit. The DOJ might not have been able to force Apple to hack an iPhone, but I shudder to think of the doxxing efforts my ISP would suffer should I actionably malign a stolid academic institution of the hard-scrabble midwest. Then again, I suppose the Circle Pines chamber of commerce could have something to say about my abuse of their moniker, or will if the Internet ever makes it north of Lino Lakes.

But I kid the Lutherans.

Calculus in Oppositeland

In Oppositeland, birds swim and fish fly. You drive on the driveway and park in the parkway, Donald Trump is a stolid civil servant, Hillary Clinton is a paragon of transparency, and people find LabKitty's political humor to be insightful.

Also, in the OL (as I like to call it) schoolchildren love calculus. Mostly because they aren't squirming sacks of hormones, but also because in Oppositeland calculators were invented before Isaac Newton. (Aside: Is it appropriate to say Newton was invented? The more you get into his biography, the more he starts to read like a piece of performance art, like Bansky, 4chan, or the Tea Party. But I digress.)

As everybody knows, before Newton came along calculus was shoulder-shrug obvious. You'd say "calculus" and the guidos hanging out at the local pizza joint would go fuggitdaboudit. (Aside: Is that term culturally insensitive? Perhaps I should have written "pizza establishment." Again, digress.)

Yes, have a seat, for it's time for another charming LabKitty math fable.

A Radar Analysis of 99 Luftballons

In their 1983 smash hit 99 Luftballons, Neue Deutsche Welle band Nena spins an ironic yarn of 99 red balloons innocently released into the summer sky triggering an EWS alert and nuclear war. The song touched a nerve in the Zeitgeist and catapulted Nena onto the world stage. German- and English-language versions topped charts around the globe and have since appeared in movies, television, video games, and the 2003 VH1 fund raiser for hurricane Katrina relief. It was even parodied as 99 Dead Baboons by Doctor Demento mainstay Tim Cavanaugh, copyright violation being the most sincere form of flattery.

The song was also a rare nod to Realpolitik. It was de rigueur in the Cold War for snarky pop culture commentary to be directed exclusively at America, the MTV generation not comprehending it takes two to saber rattle. However, Nena guitarist Carlo Karges claims the idea for 99 Luftballons came to him after watching balloons released during a Rolling Stones concert drift over the Berlin Wall toward the Soviet sector. While the US certainly deserves its share of blame for nuclear brinksmanship, go ask Arthur Koestler or Andrei Sakharov about the innocence of the USSR. When you protested outside SAC you got on the cover of Newsweek. When you protested outside of RVSN RF you got sent to the gulag.

Ping Pong Ball

My physics textbook claims the energy released by fission of one uranium atom is sufficient to make a grain of sand visibly jump. That may not sound like much, but 235 grams of U235 contains an Avagadro's number of nuclei (6.02E23) and about 5 kilograms of U235 fissions when an atomic bomb detonates (depending on the efficiency of the design, which I assume is Little Boy because we don't use U235 in bombs anymore. But I digress). My back of the envelope calculation says that's something in the neighborhood of 12,700,000,000,000,000,000,000,000 jumping grains of sand, which is a pretty substantial chunk of beach front property no matter how you look at it.

Captain Kangaroo was before my time, but Mystery Science Theater once recreated a signature gag of the beloved children's show in which Tom and Crow tricked Joel into saying "ping pong ball," upon which a seemingly endless stream of ping pong balls began to shower down on him. Jocularity ensued. I still don't understand the point, although I noticed a similar ritual marks the conclusion of our presidential primaries, albeit balloons rather than ping pong balls fall from the ceiling of the convention center once a candidate has been selected. If that's not a compelling argument against democracy, I don't know what is.

Nightmare at 20,000 Feet

In the classic 1963 Twilight Zone episode Nightmare at 20,000 Feet, harried passenger Bob Wilson (a preternaturally moist William Shatner) is flying coach to somewhere or other when he notices odd goings on out the left side of the aircraft. As the weather turns nasty, a gremlin appears on the wing (looking much like Dee Snider dressed as the Carpeted Man from The Tick). Things soon take a turn for the decidedly nonwhimsical as the gremlin begins ripping sundry wires and other important looking whatnot from the wing, all-the-while mocking an increasingly unhinged Bob looking on from his window seat (I like to think the director's cut featured the gremlin repeatedly making obscene gestures like the teddy bears from that Aphex Twin video).

In typical horror trope fashion, Bob is the only person on the plane who notices these shenanigans. His fevered warnings are repeatedly dismissed by uniformed crew and fellow passengers alike. Alas, I forget how the story ends (what can I say? The Twilight Zone is on late and it was a school night). What's important is that the episode's immortal catch phrase There's a man on the wing! has since become enshrined in pop culture, as surely as Don't have a cow, man! or Stuff for smart cats!

Well, there's several things wrong with this.

I am LabKitty's Left Eigenvector

It's possible to go your entire career without encountering a left eigenvector. Yes, if you're a playwright or barista, but also working in a field where the challenge "eigenvector" shouldn't evoke a shrug and a guess of German scat porn or a Soviet-era automotive product (is making more unit selling than Trabant!). Unitary isn't a church, norm isn't the fat guy on Cheers, and Jordan is a matrix form, not a basketball player. Fields where you should know better, is what I'm saying.

Believe it or not, here is a social ill we cannot blame on the hip-hop. No, this one falls squarely in the lap of the other evil of our times: mathematicians. Specifically: Emmy Noether, who was probably Emmy Nöther before relocating to Pennsyltucky from Germany, a juicy tidbit suspiciously omitted from her Wikipedia bio. Still, an immigrant conformity eminently understandable. Having spent time in Appalachia, I can state with some confidence they don't much cotton to the diacritically challenged in them parts. It didn't take a hole in the ground to put the bottom in their face, as the Cooleys wrote (albeit of their beloved Alabama).

Witness the Gaussian emerge like a greasy calf wriggling free of its mother's birth canal!

There was a time when I had committed to memory the formula for the Gaussian distribution (that time was the predawn hours leading to my Stats 101 final). And not the normalized Gaussian. No, sir. The Full Monty, complete with non-zero mean and variance.I sorta kinda remember it to this day, but I always seem to be misplacing a square root or factor of two somewhere.

To refresh our memory, here is the Gaussian in all its poorly-formatted glory:

    f_X(x) = 1/√2π σ exp(−½ [ (x − μ) / σ ]² )

Describer of all things, the Gaussian distribution is. Hewer of stone, drawer of water. The classic bell-shaped curve. The peak is centered at the mean, denoted μ, and the spread on either side is the variance (or, taking the square root: standard deviation) denoted σ. However, a question arises: Where does the formula come from? There's lots of equations that give a bell-shaped curve. Why is the Gaussian what it is? What's the exponential doing in there, for Cat's sake? And what about the rest of it?

It is here that the mathozoids will cluck their tongues and adjust their pince-nezzes and smirk that the Gaussian is Simply and Properly Derived using moments or characteristic functions or the weak law of large numbers or whatever. To which I have two things to say. Number one: Shut up. And number two: Shut up.

Do you want to hear my charming math fable or not?

Why is the Negative Binomial called the Negative Binomial?

One bumps into the negative binomial distribution fairly early in probability and statistics. Some tormentor is flipping a coin or whatever, and we seek to know how many flips it takes to get to the center of the Tootsie Pop. It's not terribly complicated, the neg nomy, which is a welcome relief, probability frequently making about as much sense as a Mozart opera.

However, the question came up the other day: where does the moniker come from? That is to say, why is the negative binomial called the negative binomial? Sure, the "binomial" part makes sense if you look at the formula, but there's really nothing negative about it. What gives?

Here is a question that can surely be answered by Google.

A two-minute Google search after which we can all get on with our lives.

Two minutes.

Tops.

This can only mean one thing: I am now filled with rage.

I Have No Horn and I Must Honk

Some say the most vile invention ever invented by inventors was weaponized smallpox. Others say C++ or the boy band.

Those people are wrong.

If there was ever someone deserving of having a time-traveling killer robot sicced upon his unsuspecting waitress of a mother (and, yes, perhaps even an Academy Award winning sequel, but not so much a third outing which undoes much of the mythology established in the first two films, even if the crane chase was a welcome return to practical SFX) it would be the inventor of the car alarm.

But LabKitty, I hear you protest, if my car does not have an alarm, the valets at Spagos will look at me funny. I may as well be driving a bicycle, and not one of those cool bicycles with the $1500 Shimano derailleurs, but one of those old-timey bicycles with the oversized front wheel and Tyrannosaurs-arm handlebars.

You say that because you do not understand what a car alarm is. Wires and electronics and motion sensors and a horn? No, that is incorrect. To borrow from Jack Sparrow, that's what a car alarm needs.

What a car alarm is, is Type-I error.