When I moved here 10 years ago, winter was a fantastically alien thing to me. Florida lacked winter as far as I could tell, so living in the Adirondack wilderness was a very new experience. Nowadays I get a horrible depressive ache as soon as the snow begins to fall. I can look outside my ice encrusted window and barely make out a melody akin to something Yoyo Ma might play after witnessing some horrible abuse involving small furry animals and his mother.

It is impossible to wake up gracefully when the cold sets in, especially in the early months when it not completely necessary to use heating. Your subconscious begins to make lame excuses for staying within the warm comfort of your own bed, and your body punishes you for ignoring them. Even showering becomes initially unpleasant as you must bear yourself naked to the chill before finally insulating yourself in hot steam and nourishing warm rain. But you must be aware of how long you stay in that state; for most of us, hot water is limited, and you must balance how long to shower and when to use the precious liquid for other things like washing the dishes or laundry. You can imagine how logistically complex all of this can get, especially if you live with others.

Newcomers tend to underestimate the amount of time one loses in preparation for even going outside. One must wear the equivalent of a space suit to walk EVA. Once ready, you are stuffed all around except perhaps the eyes and the nose. It’s as if some horrible cotton/poly and wool made monster has swallowed you whole for your protection. I feel sorry anybody who lives here suffering from claustrophobia. Once outside, the cold poisonous air fills your nostrils and mouth, freezing any bit of mucus that you had errantly forgotten to expel. If you’re wearing a scarf, remember not to wear it too tightly: your own breath moisture will condense and freeze once present enough.

I mentioned furry animals earlier. Perhaps it would be wise to mention the only rule of winter clothing involving pets: If it can’t be clawed up, it will get covered with hair.  This is true in any season, but it takes on new meaning in winter. The surface area to which a cat or dog’s hair can be applied explodes into the colder months, which of course somehow increases exposure to pet hair. You could walk to work and carry all the makings of another cat and not know it.

You learn to hate carpeted floors. Between carrying extra animals, you track in road salt which makes floor vacuuming an all day affair. This is depressing and debilitating on cloudy days as you have very little idea of how much time passes during activities. You might accidentally spend more time than necessary compensating for your pets seasonal metabolism.

Perhaps the most interesting thing is that the over all temperature depends on cloud cover or lack there of. The clouds actually insulate the lower atmosphere as well as diffuse sunlight. In effect, the depressing haze of cloud cover makes the air warmer than compared to that felt on a bright cloudless sunny day. If you wake up in the morning to a cloudless sky, remember to leave extra insulated and keep the heat on high: it’s probably below zero out. Being outside in such conditions is probably as close as any terrestrial creature can get to being on the moon.

The Fahrenheit temperature scale becomes very useful here: as it turns out, zero degrees is where brine water freezes. Since its cheap to use salt to thaw the ice encrusted roads, it’s good to know (and see) when it loses it’s effectiveness.

I’m also convinced that since this is the third circle of hell, some lower demon or damned second-rate city planner must have designed the sidewalks. The power lines are driven into the sidewalks in a way where plowing them becomes impossible, forcing pedestrians, like myself, to walk on the shoulder of the road to get to work. Especially snowy months force me closer to the road which of course increases the likelihood of getting run over by a road plow.

Though, sometimes, it doesn’t snow at all. I recall one particular winter in which it took until February for us to have any significant snow fall. It was in the negatives throughout the month of January, but oddly cloudy. The sight of ice deposition, frozen sod and a frozen lake under a cloud covered sky gave me an idea of what modern Chernobyl must look like. It was oddly silent, like every winter, but the lack of snow made it all the eerier.

It’s only early October, but it’s in the air. I can feel it. I dread it. It’s taken way too long to write this, as it will take too long to do anything in the coming months. Tea is already starting to cozy up to me over coffee. I need to cook through my fresh vegetables and learn a few new soup recipes. It’s time to pack away the air conditioner and get used to not seeing my bare feet.

The winter kills you with tranquility, It seems so peaceful yet so severe. One feels like an invalid for having difficulty coping but it’s only natural: we don’t belong here.

But if you’re not a math geek, keep reading.

I didn’t do very well in 8th grade algebra, so my parents bought me my TI-83 graphing calculator to aid me when I took the course again in 9th grade. There were plenty to go around in the classroom, but I could take mine home to play and use it for my homework. At least that’s what my parents had intended it for.

Teenagers are just childish enough to harbor a naïve curiosity for the world but just grown up enough to share that curiosity with some adult freedoms. It’s here where they do most of their damage. They go out with friends late at night, take illicit substances, and generally do whatever it takes to climb their social ladders. I wasn’t like that; middle school taught me well that it simply wasn’t worth being at the top with the peers fate had given me. It would have been a meaningless struggle for a hollow victory, but that doesn’t mean that I didn’t rebel.

Instead of social norms, I directed my rebellion towards my education, particularly towards math. Math is pretty much the only subject you’re allowed to do that in as it’s so easy to be absolutely wrong instead of being partly right like you can with History or Language arts. I tried wherever I could, but math was most rewarding. You can try out an idea and it only takes a little work to show if it’s the wrong way, especially always having a graphing calculator on hand. It was an experimental approach to education: the right approaches survived, the wrong ones fell aside.

This way, I formed a sort of mathematical vocabulary. It allowed me to “see” the behavior of any particular equation as long as I was familiar with the pattern it was put in. This ability earned me straight A’s throughout my freshman year in algebra and geometry. I decided to learn higher math on the computer that summer through programs my father had bought for earlier that year. Much to my surprise, I made it all the way through calculus in time for my sophomore year.

It was during this time that I was first introduced to imaginary numbers. An imaginary number is simply the square root of a negative number; no real number can be squared (multiplied by itself) to produce a negative result, but philosophically speaking, one ought to have a meaningful result when any operation is applied to any number, so one ought to be able to get a result by taking the square root of a negative value. Thus, imaginary numbers. Imaginary numbers are pretty much like normal numbers except that it’s value is a real value multiplied by : the imaginary identity . So if you needed something like the square root of -25, your answer would be . Another property of imaginary numbers is that they do not mix with real numbers; a number that has a real part and an imaginary part is called a complex number. If you wanted to perform you would only by able to combine imaginary with the imaginary and the real with the real yielding . To make matters more complicated, you can multiply real and imaginary numbers (even complex numbers) with one another, but since then complicating multiplication a bit. It suffices to say, complex numbers aren’t your daddy’s math, and they really weren’t in the textbooks I was given either.

Ultimately, I became curious about how equations like would behave. Now normally, looks like this

The TI-83 has a complex number mode, and when I tried to graph , it gave me this

I had apparently left Kansas sometime earlier and entered a Louis Carol novel. (Which isn’t too far from the truth)

No, it’s not the opening to the outer limits, nor is it a DNA double helix. What it is, though, is what could be called a metric wave function. Waves can be produced with trigonometric functions like sin or cos but they did so for a reason. Though, I had no clue why it looked this orderly for , but I didn’t know what to expect in the first place. What I found truly bizarre was that the real part of matched up exactly to . To make matters worse, there was no algebraic, trigonometric, or even calculus method I could use to figure out why it turned out like this.

It took me until the beginning of my Junior year to figure it out.  I flipped to a page on Taylor series polynomials 2 weeks into actually taking Calculus. Fairly quickly, I realized there was an intimate relationship between and trigonometric functions like and . After another week of wrestling with the algebra of Taylor series polynomials, I had found my answers.

This is Euler’s equation. Simply, this equation illustrates that there is a natural mechanism in mathematics that ties two very desperate things in a simple and elegant way. That there is a transcendental link between rectangular coordination and polar coordination. More generally, it can be viewed as .

To me, it was the most beautiful thing in the world. No matter how wrong you tried to make something in math, there was always an answer, and the harder you tried to break it, the more beautiful it became. From Euler’s equation, one can make this identity:

Illustrating the link between 4 fundamental values of math: e (Euler’s constant, used for evaluating continuously compounding interest), , i and -1.

Don’t worry if it doesn’t make sense to you. That’s a part of the beauty though, one can rationally access and use a vocabulary of knowledge that is beyond our ability to directly abstract. Even in my mind, I have to remember that the i in the exponents position connotes an entirely different pattern than that associated with real numbers. While it’s common in english, you almost never have mathematical equivalents to “slaughter” and “laughter”.

So anyways, It was about this time that I had gotten involved in ISTF at school. They wanted me to have an aim account to support communication online among the other team members, if you’ve made it this far, then you understand how obvious and stupid it was. But I typed it, exipolar, and it’s been stuck with me ever since.