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World Eigenvalue Day

Updated on February 15, 2017
Day of Days!
Day of Days!

LabKitty Presents...

Before man was, eigenvalues waited for him. The ultimate trade awaiting its ultimate practitioner.

When the Earth formed, when the mountains rose, when the land granted purchase to the sea and the sea returned life to the land, eigenvalues were there. When the Cretaceous terror slashed a gap in the firmament through which misery poured upon the living. When men did meet other men and first smelted metal, when the wheel turned machines and made gun barrels, eigenvalues were there.

There they waited. Patient. Silent. Resolute. Since before our sun burned hot in space and before our race was born, eigenvalues waited.

They waited for a question.

Now, lo these many eons later, eigenvalues course through modern society like wine through a goose. As we play out the insignificant comings and goings of our everyday life, they stand a post. In the CMOS of your On-StarĀ®. In the corrective lenses of the Hubble. In the laughter of children.

Like a sleek, vigilant puma: eigenvalues.

But do you appreciate them?

No, you do not.

World Eigenvalue Day

Well it's about time eigenvalues get some love. The good news is you can atone for your shameful neglect by joining LabKitty's efforts to establish World Eigenvalue Day! A day of celebration and jubilation for all things eigenvalue. A sort of cross between Comic-Con and Pi day. Part barn raising, part virgin sacrifice. A Planting Festival cum Solstice Celebration, as it were, with drinking and parades and drinking.

Feburary 14th is World Eigenvalue Day. For there is no greater love than self-love.

The bad news is there's still a few small problems left in getting the world to celebrate World Eigenvalue Day. Getting the world to celebrate World Eigenvalue Day, for one. But be not discouraged. Think of the humble beginnings of holidays we now take for granted. Whacking Day began as an excuse to beat up the Irish. Thanksgiving started with a few lost Puritans and a stack of smallpox-infected blankets. Mardi Gras was originally an NINDS study.

What's stopping us? Nothing at all, really. We have nerds, the Internet, and LabKitty, a kind of Matryoshka doll of reckless enthusiasm where nothing is beautiful and everything hurts and I think I'm quoting that backwards.

It's time to get this party started.

Eigenvalues in Popular Culture

Yeah, the eigenvalue is off. HATE WHEN THAT HAPPENS AMIRITE?

Source: Open Clip Art Library
Source: Open Clip Art Library

Interlude - Wait, eigenvalue, what?

What's that? You say you don't know what an eigenvalue is? You poor thing. How could you have allowed your alma mater to leave you so tragically unprepared for life?

Still, instead of dwelling on the fact that you're late to the party let's focus on the fact that you've shown up at all.

The official definition of an eigenvalue (the scalar multiple representing a linear transformation when expressed in a special coordinate system) is about as helpful as describing Baby Got Back as a time series of variations in air pressure. So instead, allow me to tell you a fable (an eigenfable, if you will).

Once upon a time there was a village, and next to the village was a river. The river did not flow from north to south nor east to west. Neither did it flow from south to north nor west to east. It just flowed the way it did and the villagers never gave it a moment's thought. This because all roads in the village lay either parallel to the river or at right angles to it.

If a stranger appeared, say, asking directions to the bagelry, a villager might respond thusly: "Good Sir, you walk toward the river three blocks, along the river four blocks, then away from the river for a block." Here in the telling the villager would hook a thumb though the button-hole in his hair shirt and look wistfully off into the distance. "There you may procure the finest bagels in all the land," he would proudly beam.

One day the King came to town. The King brought with him a Sorcerer and the Sorcerer brought with him a device. The device looked to be a pocket watch, but on the face -- where the numbered hours should have appeared -- were instead inscribed only the names of the four conjectural winds, in clockwise ordered North, East, South, and West. Above these floated a black needle, which by unknown majick did always point to North, nonirregardless of which however way the Sorcerer waved it about. Clearly, this was an evil thing, and the villagers began to wonder aloud just what the heck the NSF had been doing with all those chickens and other tax sundry they had demanded over the years.

The King raised a hand, silencing the twittering of the crowd. "My people!" he called out. "Henceforth shall ye navigate by this device, for it imposes upon the land a dividing up into north-south and east-west directions. You shall use these directions, and these directions are the ones you shall use. No more of this river-direction talk, or whatever the heck it is you backwater yahoos call your primitive system of circumnavigation."

Upon hearing the King's proclamation. a great roar came from the crowd. Ramsock the Barrel Maker roared loudest of all. "But, Sire!" he roared. "Your system of dividing-up is unnatural! Consider ye this: At present, should need arise, say, to send my barrels to the bagelry, I simply tell the barrel-herders to go downstream for a furlong, then away from the river for seven blocks. Using your Sorcerer's devilry, "downstream" will become south-east, "away from the river" will become south-west and "toward the river" north-east. Or is it south-south-east or north-south-west? I know not, for who can reckon such things?"

There followed a chorus of spittle-flecked disparagement directed against the King, accompanied by obscene gesturing and suggestions demonstrating a profound ignorance of anatomy.

"You are attacking our values!" Ramsock shouted over the din, now beating a pitchfork against his breast for dramatic effect. "You are attacking EIGEN values!" Ramsock bellowed, this time using his native tongue which we've assumed is Germanic for illustrative purposes.

The King, though dismayed with this rather ham-fisted third act, recognized the need to wrap things up. Thus did he relent and permit the villagers to navigate according to their simple system of eigenvalues for the rest of their days.

The End.

Eigenvalues in Popular Culture

For the fable-impaired, here's a more sober introduction to eigenvalues from YouTube staple BlueBlueBlueBrown. A bit longish, but well worth it. Eigenvalues!

The Eigenvalue Song

Is there an Eigenvalue Day song? Of course there is! What else would we bellow as we raise our flagons? There is a libretto, but, alas, we still require a melody. So for now, just imagine the EvS being shouted, in unison, at the top of your lungs, and probably drunkenly.

Eigenvalues, sing along

As we sing the eigensong

EISPACK, LINPACK, Recipes

Give us eigens if you please!

Eigenvalues are our friend

Every time we think of them

Normal modes and free vibrations

Simplify the computations!

Eigenvalues are our hero

Make determinants a zero

If you need them really quick

Invariants will do the trick!

Eigenvalues, above all

Make the world diagonal

If defective you'll be warned

'cause you'll get a Jordan form!

Eigenvalue Song Glossary

In case you may be trying to craft a tune to go with the EvS libretto, below you will find a glossary of terms appearing in the Eigenvalue song to help guide your efforts in song-craftery.

Defective - a matrix that does not posess a complete set of linearly-independent eigenvectors and is therefore not diagonalizable.

Diagonal - a matrix whose only non-zero entries appear on the main diagonal.

EISPACK - a free software library of linear algebra routines, including those for the computation of eigenvalues and eigenvectors, developed and distributed by Argonne National Laboratory.

Free vibration - vibration of a structural system in the absence of loading (as opposed to "forced" vibration).

Invariant - matrix quantities such as the trace and determinant that are not altered by linear transformations.

Jordan Form - a block tridiagonal form that is the computational homologue of diagonal for a defective matrix.

LINPACK - see EISPACK

Normal Mode - a computational approach for determining structural vibrations in which the overall motion of a system is expressed as the superposition of elementary motions defined by the eigenvectors of its stiffness matrix (the "normal modes").

Recipes - nerd shorthand for programming bible Numerical Recipes by Press et al.

Eigenvalues in Popular Culture

Eigenvalues + Tom Jones = World Awesome Day!

Eigenvalue Day Gift Giving Traditions

Which brings us to gift giving. As Adolph Hallmark famously said, it's not a holiday unless money changes hands. From Black Friday to the annual President's Day sale at the mattress store, gift giving is tradition. Heck, I suspect some of you have recently purchased candy, flowers, and pregnancy tests, preparing as it were for that other, lesser, Feb 14th event.

So LabKitty put in much time and effort assembling proper Eigenday gifts. Begin with a simple Eigenday pin, announcing your conversion and creating confusion in the world around you. Then, add an Eigenday shirt, with proud logo on the front and Eigensong lyrics on the back. Complete the trilogy with an Eigenvalue Day mug (an eigenmug, if you will). An everyday reminder to watch the calendar year round from the confines of your cubical, as the approaching day of day bleeds sunlight into your otherwise dark little life.

Finally, for advanced revelry, there is the Eigenvalue day drinking tankard. An old school flagon, designed with the serious eigenvalue enthusiast in mind. Available in two styles, and with the opening lines of the Eigenvalue Day song printed on one side, a mnemonic that, trust me, becomes ever more helpful as the night progresses. Perfect for karaoke!

Visit LabKitty on Zazzle for all your WED gift-giving needs!

Postscript

We have a date and a song (and gifts). There's not much more to be done except take (or purchase) these and run. If all Abe Lincoln had to do was chop down a cherry tree to get us a day off from work, what stands in the way of Eigenvalue Day? Not since the Super Bowl has the world had opportunity to create a new sacred holiday.

Eigenvalues!

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