Once Upon a Time Warp (A Brief History of Leap Day)

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It’s a tale as old as time: one of the greatest innovations of human timekeeping is credited to “Father of Leap Day” Julius Caesar, and where did he get the idea? From a woman.

Gather round, kids, for a brief story:

Once upon a time, there was a Prince with a Problem. His people, the Romans, were having some trouble keeping track of things. They, like most of humanity, had adopted a lunar calendar – first with only ten months (because, in a move that would make George R.R. Martin proud, winter was a “monthless time”), then eventually with January and February to bring it to twelve. But if the Prince and his countrymen had bothered to ask, any woman could have told them that letting life be ruled by a lunar cycle is just asking for trouble. And it was!

The Prince’s trouble was that the Man on the Moon takes on average 29.5 days to complete one of his cycles, which makes a 354-day year. Mother Earth, on the other hand, has more to do; she takes roughly 365.25 days to get all the way around the sun, which made the Roman calendar a full 11.25 days too short. Bummer. In just a few years, this communication gap had the Ides of March on the Ides of April, and that just sounds silly.

Like the Classic men that they were, the Prince and his Romans routinely ignored this inconvenient problem until it got so big they couldn’t; then they “fixed” it by inserting a random extra month into the year now and then, forcing that rascal Spring back where it was supposed to be.

Effective? Yes. Functional? Maybe. But much like a frat house, this was no way to live.

In a different part of the world, a Queen named Cleopatra and her Egyptians had devised a brilliant strategy for living in harmony with Nature. They kept a calendar of twelve tidy 30-day months, then made up the extra length with a five-day party at the end of each year. Every fourth year, that party went for six days.

Kids, if this sounds like the best idea humankind has ever had, you are right. We really missed the boat.

By the time Julius Caesar met Cleopatra, things had gotten way out of hand for the Romans. I mean, seriously out of hand – they’d ignored their time problem so long that Spring was hiding in Summer and snow was falling in May. Julius was impressed by Cleopatra’s brilliant calendar (and by everything else about her, pretty much), so he did what usually happens in these situations: stole it from her, made it a little less good, and proudly declared it his own. Typical.

First, Julius had to get his Roman calendar back on track, which could have happened by letting time take its course, but was more fun to do with brute force. (Bruté force? That would come later.) Declaring 46 B.C. the “Year of Confusion,” Julius Caesar made it 445 days long and forced that sneaky Spring Equinox back to March, where it belonged. He then sprinkled some extra days around the calendar (making his own month the biggest, of course), and decreed that every fourth year one extra day would be added to the end – which, for the Romans, was February.

Way to kill the week-long party, Julius. Way to kill the party.

And everyone lived happily ever after in harmony with Nature – except that they didn’t. There was a dark storm brewing, and it was called Accuracy. You see, kids, the problem is that Mother Earth only takes roughly 365.25 days to circle the sun. She actually takes 365.2422 days, which means that adding a full quarter day to every year then made the Roman calendar 11.2 minutes too LONG.

This seems like a small problem, sure, but like grains of sand in an hour glass, it adds up. In 128 years, the whole calendar was off by a full day, and by the time of Pope Gregory XIII more than 1500 years later, that sneaky bugger Spring was back in April instead of March.

Once again, the man in charge took drastic measures, removing ten days from October 1582 (no Halloween candy for you, kids), and declaring that, going forward, every century year – 1600, 1700, etc. – would have no Leap Day, unless that year was also divisible by 4.

That’s right, kids; bet you didn’t know how special that Leap Day was in 2000.

And so, with this new “Gregorian” calendar (because of course he renamed it after himself), we’ve got the whole 365.2422 days per year problem sorted out. For a while, anyway. It’s still not perfect, but it will be 3,300 years before we’re off by a whole day again. Let those guys worry about it.

The End*

*Or is it? The buried feminine roots of Leap Day seem to have caused some residual guilt that has seeped out in the form of misguided attempts at female empowerment. In Ireland and the U.K., Leap Day became traditionally the one day women were allowed to propose to men – and had to be compensated (with money or clothes) if turned down. In the U.S., this tradition became “Sadie Hawkins Day” (celebrated November 15th in common years), and in one city – Aurora, IL – single women are deputized on Leap Day to arrest men.

THIS YEAR, I say we tackle our own empowerment in a less condescending way, and use our special day to leap a woman one step closer to the Presidency. Tomorrow is Super Tuesday, after all – and the first day of Women’s History Month. Make some history, Hillary; one giant Leap for womankind.

Give Thanks to the Time Lord

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Exactly 100 years ago, an alien mind inside an unusual man opened the eyes of humanity and forever changed the way we see the universe. His name has become synonymous with Time and Relativity and Space, yet his face has appeared to the world in many different forms.

No, I’m not talking about The Doctor. At least not the one from Gallifrey.

Much like the Tenth and Eleventh Doctors, though, Doctor Einstein was also a hipster icon of his day. He may not have worn Chucks with a suit or made bow ties and the fez cool, but he did rock a thrift-shop wardrobe, some seriously crazy hair, and a retro bicycle as his regular ride.

Einstein was at times a frustrated genius, burdened – like the first few Doctors – by the inability of mere mortals to keep up with his intellect. He could also be patient and calm, like the Seventh Doctor, or grumpy like the Twelfth, and occasionally scare the shit out of people, much as the Fourth Doctor traumatized my childhood (no thanks to my older brother’s TV habits).

Like the Ninth Doctor (and the uncounted incarnation before him), Einstein was often a man reeling from and railing against war. But he also never lost his sense of whimsy – his inner Sixth Doctor – or (for some of us weirdos) his romantic appeal, like the Eighth.

Doctor Einstein saw and solved problems no one on this planet even conceived of, by keeping his mind open and letting his imagination lead the way. He quite often failed on the way to success, and knew that sometimes it is best to blow things up in order to put them back together much stronger. And 100 years ago, over the four Thursdays in November, 1915, he presented to the world his theory of General Relativity – quite literally creating the fabric of space-time with his mind.

I like to think of Einstein as the Zero-th Doctor – because any mathematician knows that counting really starts at zero, not one.

So today, as we celebrate family and friends, eat delicious meals, and give thanks for all that we have in this universe, spare a thought for the wonders of science. For the spaces we gather to share food, the gravitational pull that draws us together, and the time that slows down when life is really good.

And give thanks for Doctor Einstein, who opened our eyes to it all 100 years ago today. He is truly the original Time Lord.

Number Munching

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There need to be more math-inspired food holidays, and together you and I can make that happen.

Wasn’t Pi Day fun? Even though this year (3/14/15 at 9:26:53) was the Pi Day of the Century, March 14th is a great excuse to eat pie in any year. But, just as they say that there are 10 types of people in this world: those who understand binary and those who don’t, the world is also divided into those on team pie and team cake.

As much as I love the number pi, I am decidedly a cake girl. It was the source of great friction in a relationship once, even after I baked a Cherpumple to bridge the gap with my pie guy. (A Cherpumple is a cherry pie baked inside a chocolate cake on top of a pumpkin pie baked inside a spice cake on top of an apple pie baked inside a vanilla cake. It is a foot tall, weighs 18lbs and feeds about forty. Epic.)My Cherpumple

So what other math-food holidays can we celebrate, preferably without sparking dessert wars?

We can stick to the irrational number world and celebrate “e Day”. Since e is the natural log, we could eat ants on a log, cheese logs, yule logs (the cake kind) and basically any other roulade. But e is approximated as 2.7, and February 7th has come and gone.

Famous ratios might be the answer, like the Pythagorean Theorem’s “a squared plus b squared equals c squared” relationship between the sides of a right triangle. This gives us the classic 3:4:5 triangle ratio, so we could have eaten triangular foods (pizza, baklava, candy corn) on March 4, 2005 (3/4/5) or June 8th, 2010 (6/8/10). Unfortunately, Pythagorean Theorem days require all three numbers, and even though the next one is September 12th, 2015 (9/12/15), I’M HUNGRY NOW.

Square root dates have the same need for three numbers that makes them rare – such as 2/2/4, 3/3/9, and next 4/4/16 – and besides, do we want an entire meal made up of root vegetables?

There is always the Fibonacci Sequence (my personal favorite), which runs 1,1,2,3,5,8,13… etc., adding the preceding two numbers into infinity. This number is traditionally celebrated on November 23rd (11/23), but could also be feted on 1/1/23 when it comes. Since Fibonacci formulated the sequence after a thought experiment about mating bunnies, we should all make like Elmer Fudd and hunt some wabbit.

Or, since the Fibonacci Sequence also defines the Golden Ratio – another irrational number, roughly 1.618 – we can celebrate the hell out of it on January 6, 2018. The rich can eat foods dusted in gold flakes and gold powder; the rest of us can meet up at McDonald’s.

Still, these dates are years away. I want math-inspired food NOW!

Our answer is the humble mole. Not the blind, hole-digging insectivore, nor the irritating, cancer-threatening skin growth; I mean the massive constant defined by the number of molecules in 12 grams of Carbon-12 – specifically 6.022 times 10 to the 23rd power.

Think about it: a mole is a unit of measurement in chemistry, and mole (“mo-lay”) is a delicious Mexican sauce made with chocolate and spices, so the food tie-in is natural and fantastic. Plus, the number of things in one mole of anything (6.022 x 10^23) is also known as Avogadro’s Constant; ‘Avogadro’ is so close to ‘avocado’ it’s like the food gods are daring us NOT to do this. A mole dish with avocado? Yes, please!

Finally, Amedeo Avogadro (for whom the number is named) was an Italian Count born in 1776 (freedom!) who studied and practiced law (litigiousness!) before inheriting his father’s title and enough money to retire and dick around with science (financial privilege!). What’s more American than that? This should absolutely be a national holiday.

Oh, sure, I know people already celebrate Mole Day on October 23rd at 6:02, but just as some people celebrate Pi Day on July 22nd (because it can also be approximated as 22/7 and Europeans write their dates day/month), we can certainly have two Mole Days. And, yes, it would make more sense to do it on June 2nd instead of June 22nd, but I missed that day, so screw it.

JOIN ME on June 22nd at 10:23 (am or pm is your choice) in eating a delicious Mexican dish of any type so long as it is slathered in mole sauce and accented with avocado.

It will be MOLE-ecular gastronomy at its finest. Bon appetit!

Pompous and Circumstantial

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Natalie Portman gave the Class Day address at our mutual alma mater last week, and despite her nerves she did a ‘Professional’ job (okay, I’ll stop). It was refreshing to hear her recount the experience of first setting foot in such an overwhelming and impressive place full of overwhelming and impressive people – and comforting to learn she made many of the same mistakes I did.

The world is full of brazenly confident people, and Harvard Yard has more than its fair share. For Natalie, there were five different peers who announced on day one that they would be President someday; I only remember two in my first days, but we both believed all of them from the sheer force of their conviction. Bold declarations are impressive, and those of us not in the habit of making our own are inclined to be won over by their swagger.

(This is the only explanation for a particularly disastrous dating choice of mine freshman year; he told me he was the smartest, funniest guy in the room and I believed him.)

As I quickly learned, though, there is no guarantee of any substance behind the bluster. For every Babe Ruth who backs up a called shot there are a dozen Donald Trumps who are full of shit.

Both Natalie and I reacted to our bold new world in the same way: by letting it intimidate us. We accepted these people’s brazen visions of the world, their standards for greatness, and their definitions of success. Instead of asking ourselves what we wanted out of school or life, we worried about not being good enough – and once someone else is allowed to make up the rules, there really is no way to come out on top. Just ask any six-year-old.

In this past year, I have been drawing inspiration from Albert Einstein’s “Annus Mirabilis” (1905), in which he published four papers each of which was a major breakthrough in its own right. One of the recurring themes in discussions of his unparalleled achievement is the complete unwillingness Einstein had to ever accept any unproven principle as a given. Because he refused to believe time was an immutable constant simply because everyone else assumed it was and no one had seen evidence to the contrary, he was free to explore his own imaginings and now the world understands relativity. You’re welcome, world.

When we free ourselves from belief in how things are “supposed to” be, we open the door to far deeper understanding and far greater achievement. As Natalie put it in her speech, we should remain ignorant of the limitations the world has assumed for us. Or, as that six-year-old would put it, “Sez who?”

Look to the bumblebee for inspiration. For centuries, the world of physics expended a great deal of energy and hot air over the fact that a short, fat, fuzzy insect with stubby wings should not be able to fly. And yet they fly anyway. Mainly, as mathematician Sir Michael Atiyah pointed out, because a bumblebee does not understand the laws of thermodynamics. It simply doesn’t know it can’t fly.*

[*Also, as has recently been determined, it doesn’t flap its wings up and down like other flying things but rather front-to-back with a slight tilt, as though treading water. This creates mini hurricanes above each wing, with low-pressure centers that make it easier to stay aloft. But “because of ignorance” is more romantic.]

If Forrest Gump taught us anything, it is that if we dive into that box of chocolates listening to cries of “beware the cherry cordial” and “butter creams are the best”, we will very likely be disappointed, but if we go in hoping for a sweet treat, we will probably get one. At least I think that was the point.

In other words, don’t believe everything people say (especially about themselves), don’t believe everything you think (especially about yourself), and – to borrow from Stephen Colbert’s commencement address at Wake Forest – define your own standards for success and happiness. Then go for them. Everyone else can go suck a cherry cordial.

Time Weights For All Man

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AlTime is a flat circle. No, wait; Time is an increasingly desperate “news” magazine. Time is an herb to the blind and spelling-impaired?

Time is all of these things, and also none of them, for time – like color and popularity – is merely a product of our own perception.

We know this because 110 years ago a bored 26-year-old patent clerk started daydreaming and ended up having the best year of his – or of anybody’s – life. It’s a good thing there weren’t more people inventing things in Bern around 1905.

Exactly 110 years ago this month, that bored patent clerk – who was still bored even after publishing a paper in March that would become the foundation for quantum physics and another in early May about Brownian motion – started thinking about Galileo and Newton, and how the motion of objects is relative to the motion of an observer. He then asked a question no one else ever had: What about light?

That got him daydreaming about speeding trains, and the universe was changed forever. Literally.

[What is it with men and their fascination with vehicles? Galileo and Newton determined relative motion by thinking about boats (while a man walking on a ship’s deck may travel 10 meters in 10 second from his own perspective, he travels much farther to a person on shore also watching the ship sail by), and Einstein used trains to show that a beam of light bouncing from floor to ceiling travels one distance to an observer on the train but a longer distance to an observer watching the train from a hill. Boys and cars, man. It’s genetic.]

By the end of June, 1905, Albert Einstein had published his Special Theory of Relativity, which stated that if light truly does always move at a constant rate (which experiments had shown but scientists had been reluctant to accept), then time must be just as relative to the observer as distance and motion and acceptable fashion standards (shoulder pads, anyone?).

Suddenly, a clock was nothing more than a series of countable moments; a second merely an agreed-upon unit that only stays consistent so long as we remain still relative to the time piece. As soon as we accelerate that clock out the window, those seconds get longer. So…time doesn’t fly as it flies.

Our bodies already know this; the heart is a clock, beating out a series of countable events, and the faster we move the slower time progresses. Stay active, stay young.

Before 1905 played out, Einstein managed to blow minds open one more time by proving that mass and energy are on the same spectrum (or, as it is more commonly known, that energy (E) equals mass (m) times the speed of light (c) squared). This equation gave us the power (nuclear power) and Einstein the ability to reach his most influential deduction of all – which, given his work thus far, is certainly saying something.

If light is energy, he thought, (paper one) and energy has mass (paper four), then light has mass and should be affected by gravity (it is – eventually, in 1919, a solar eclipse allowed experimenters to prove that light does indeed bend its path when traveling past a large body such as the sun). And if the path of light is bent by gravity, Einstein continued, then so must time be affected (paper three).

It took a decade to work out the math, but 100 years ago this November Albert Einstein was able to present his General Theory of Relativity, which tied the fourth dimension (time) to the three we already knew so well (space) to introduce the idea of Space-Time as the fabric of our universe. A fabric that, like a fabric should, gives and curves around heavier objects. The larger a mass, the more it tells both space and time to “get bent”. That’s gravity.

So if time, like light and space and anything else with mass, is affected by gravity, it makes sense that time itself has mass. Finally! That explains the Sunday evening doldrums, when the weight of the weekend that hangs behind us requires a Herculean effort of will to drag into Monday morning.

It also explains why, as I try to fall asleep some nights, I can physically feel those ounces of time passing through me – from future, to present, to past – adding their weight to the ever-increasing mass of time that lies behind. One. Heartbeat. At. A time. How much farther must I carry that weight toward the unknown destination in my future? Can I keep moving forward as it keeps getting heavier every day? At what point will it weigh too much and drag me to a complete standstill – or backwards?

On these nights, I find it comforting to remember E=mc2 and the fact that the accumulating mass of my past also increases its potential energy. The longer it takes me to get…wherever, the brighter I can burn when I do.

Other times, I just roll over and find a fuzzy cat ass in my face. A cat ass in the face is pretty much the best life has to offer anyway, so what’s my hurry?

Noisomes Off

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If I could have one superpower, I would choose the ability to blink leaf blowers out of existence with my mind. My faithful sidekick would do car alarms. We would be The Sound and The Fury – fighting for peace, quiet, and the manual way.

Leaf blowers are stupid, especially in the city. They accomplish no more than a rake or broom, in barely less time, and do it all while polluting the air with ear-splitting noise and filthy dust. Gas-powered leaf blowers (which is most of them) do all of that while also spewing toxic fumes, making them simultaneously noisy and noisome.

‘Noisome’ is one of those words that makes no sense, because it should mean “loud” but instead means “offensively stinky or unpleasant”. That dissonance, though, is what makes it the perfect word to describe the current state of communication in our culture.

We have a problem with noisome discourse – increasingly disagreeable, foul, and loud – and just like the leaf blowers, the problem is largely fueled by GAS:

GENERALIZATIONS – all of which are terrible. (See what I did there?) Too often we inflate our arguments by shouting that “all cops are bad” rather than “this cop is bad” or that “all men are pigs” when at the moment only that man is a pig.

[Why is ‘pig’ a derogatory term? I love pigs. They are smart, and clean, and taste like bacon. We should all be pigs!]

The problem with arguments inflated by generalizations is that they are easily punctured by a single anecdotal counterexample – thus letting the air out of what may otherwise have been solid logic.

ASSUMPTIONS – which not only make asses out of us, but likewise also leak a noxious stench into the air. When we hear words leave a fellow human’s mouth these days (or see them typed), our instinct seems to be to immediately assume the most racist / sexist / elitist / ageist / atheist / anti-whatever-ist intentions behind them. Sure, taking offense is fun, but why not allow for the possibility someone is curious, mistaken, or just plain dumb instead of horrible? Assumptions are dangerous; it only takes a single spark of defensiveness to ignite an explosion of anger and send civility up in flames.

SELFISHNESS completes the toxic triumvirate in our GAS. Not just “shut up and let me talk,” selfishness, or the “my way or the highway” variety; we have also become selfish in our refusal to accept partial agreement or any personal fault. High on the fumes of our own opinion, we focus all our attention on winning that last minor point against an ally instead of working with them to battle the larger problems facing both of us. As with any gas, the overall pressure of selfishness increases as the force of our need to be 100% right gets divided by a smaller and smaller area of focus, ultimately resulting in a blowout.

This chemical cocktail of generalization, assumption, and selfishness is fueling a lot of sound and fury in our world today.

As science has shown, GAS will, once released, expand to fill any available space. It may not seem harmful at first, and is even tempting since GAS can burn colorful and bright or give us a quick high that makes life briefly hilarious. But it is not healthy to breathe and can quickly turn dangerous, which is why we should stop releasing GAS entirely.

It won’t be easy. GAS is often hard to hear, mostly impossible to see, and no one ever wants to admit it comes from them (even though we all do it). But GAS is filling our world with an odious cloud that is highly combustible, poisonous to ingest, and toxic to our environment.

On Earth Day, let’s all stop spewing this GAS into the air and let clearer heads prevail.

In the Blink of an Einstein

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TEN… By the time I was ten, I was madly in love with Albert Einstein. I have no idea how I even learned about him in the first place, but the source of my love was obvious. He was mischievous yet deeply profound, musical, passionate, curious, kind, odd looking, and more than a little alien; that is a vibe I could dig. My taste in men hasn’t changed much since.

NINE… In 9th grade, I decided to finally understand the Theory of Relativity. (Enough to do a report for school, at least.) My favorite illustration of how time is relative involves a flashlight and a train:

Imagine a light shining up from the floor of a moving boxcar, to a mirror on the ceiling. Turn the light on and it hits the mirror, bounces, and returns to the source. To an observer on the train with the light, the beam travels a distance equal to twice the height of the boxcar (up, then down).

But to an observer on a hill watching the train go by, the light travels further. Its journey isn’t just up and down, but also the horizontal distance the train travels in that time. To the observer on the hill, the light’s path is two diagonals of a triangle whose base is the distance traveled by the train and height is the height of the boxcar.

Since Rate (speed) is equal to distance divided by time, and since the speed of light is always the same, the fact that the light travels different distances means it also does so over different times. To the observer on the hill, the light’s journey took longer. More time passed than did for the observer on the train, even though they were both watching the same light.

EIGHT… This principle of relative time was demonstrated for a much wider audience in the 80’s, when a different Einstein – Doc Brown’s dog – spent a few seconds in a speeding DeLorean that simultaneously lasted a full minute for Marty McFly.

SEVEN… Any tween who was ever forced to play Seven Minutes in Heaven already understands the relativity of time with excruciating clarity. How slowly those seven minutes pass when we are awkward and self-conscious. Yet when I met Hodor earlier this year and we set a kitchen timer to 20 minutes on our second date (an attempt to wield some grown-up control over our teenage attraction) we were suddenly on a speeding train. Those minutes passed in seconds, and we had to reset the timer at least three more times to test its functionality (for the sake of science, of course).

SIX… I once even experienced the entire life-cycle of a relationship over the course of a six-hour conversation. Via text. It started as a chat about a basketball game, during which we acknowledged our usually moderate flirting had escalated to blatant, and then both admitted we were very interested in the person but not currently ready for the relationship. The raw honesty on display made me far more interested than at the start of the conversation, and our subsequent discussion about how to conduct ourselves in the future felt like passing through a break up and coming out the other side. In the course of one night, I gained an amicable divorce.

FIVE… Time is relative everywhere, not just in love (though especially in love). When I teach a five-hour logic class, I am most definitely on the train. Passage from start to end seems to take no time at all – though I know we traveled because I finish exhausted. My poor students experience the full expanse of the time, however, watching from the figurative hillside.

FOUR… Soon, we wave goodbye to the year 2014, a year full of time quirks. Looking at the bulk of events, we seem to have both traveled far and stood still. A lot of ugliness we thought was behind us turned out to be very present. But at the same time, the fact that we are now talking openly about things like religion, drugs, law enforcement, homophobia, sexism, racism, principles and so on is a huge step forward for our community.

THREE… For the first three months of 2014, I was an observer on the hill, living more life than my counterparts on the train. On January 1st I was a single girl between projects; by the end of March I had hundreds of regular readers and had both met and fallen completely for Hodor. For the last three months, I’ve been back on the train; Hodor left in September, but it feels like only days ago to me.

TWO… Career-wise, I ticked off a second full year of waiting for the biggest deal of my professional life to finalize. It is my own personal Groundhog Day – stuck reliving February 2nd when February 3rd is the day life starts. I fully understand why Bill Murray’s character experiments with violence in that movie.

ONE… December 31st is only one night, but somehow we imbue it with the weight of an entire year. With so much time passing in an instant, it is easy to feel bruised by the impact. But it is important to remember that the real significance of New Year’s Eve is…

ZERO. In almost every sense. It is nothing, a place-holder, just another day; it is also something, a baseline foundation from which to build another year. Zero can add nothing, nor can it take anything away. Yet it has the power to multiply things exponentially, or to negate them entirely.

It’s all in how we choose to use it. So, I say we use December 31st for a little bit of reflection, a whole lot of appreciation, and a healthy amount of celebration. Travel on the train or off, but remember it is still only one night, much as zero is only one number among many.

As long as zero isn’t also the amount of champagne left for drinking, everyone will be just fine.