Robin Does Everything – Back From the Psych Ward

I did a bit of remodeling on my YouTube channel. The Crazy Addict is no more – although I didn’t know it yet when I made this video – and in its place is a new series, which I will use primarily as a vlog to document my victories and defeats in my quest to relearn what my capabilities are after eight years of mental disability, and return to the arena of functional, productive human beings.

What is a “Train Poem”?

Today I wrote my first train poem since senior year of college. Since I am woefully out of practice, this is the first of my train poems to have a literal train in it, for expressive assistance.

Since train poems don’t usually involve actual trains, then what are they about, and why do I categorize them as such? Train poems are about people. (Very occasionally they are about experiences – for example, I have one train poem about softball.) Trains are incredibly powerful, complex, inspirational and awe-inspiring marvels of engineering, and so are the human subjects of my train poems. When you are about to be hit by a train, there is little else you can do with the last few milliseconds of your life than appreciate the train’s majesty. I compare the impact of certain people on my consciousness to the impact of a train on a body, an impact so forceful that there is little else I can do than be inspired to write poetry. The impact splatters my insides onto paper, if you will. That’s the idea behind Freight Special, the juxtaposition of poetry with pictures of trains. (Freight Special is a poetry compilation that’s been in the works for about a year and a half, though its publication will require me to *actually finish a project*, so there is little hope for it to take its place on your coffee table.) This poem, like I said, is sub-par, so it won’t be in Freight Special, but it is a good illustration of the concept.

You stand on the tracks
At the top of the hill
And bowing in reverence,
The world becomes still.

The train commits blasphemy
Hurtling unchecked:
A parallel god
Of a variant sect.

Yet scopic and thoughtful,
The color of coal,
Your eyes have the volume
To swallow it whole.

The train is a regent,
A diesel showstopper,
While you are an ambience
Cloaked in soft copper.

One metal juggernaut,
One noble tower:
Power meets majesty;
majesty, power.

 

You leap from the tracks
And the train passes by.
You named it the victor —
I cannot see why.

Marathon Fantasy Land

As you know from my previous post, a couple weeks ago I ran a marathon. As you may have been able to pick up from this blog in general, I was born in the ‘hood and spent periods of my life in rather extreme poverty, and the present day is no exception. Also, though I like to think of myself as a big ol’ teddy bear who don’t care what nobody thinks, I am quite the chronic stress machine. And my life has done nothing to relieve that lately. So what do I do? I run from my problems. I’d say I need a hug, but I already get about ten hugs a day because I live with my boyfriend. What I need is bigger than a hug.

Which is why I’ve spent the last few days in Marathon Fantasy Land, where I have the funds to run every race I desire and I consequently run a marathon every weekend of my life. That is apparently now where I go when reality forces me out. It used to be Mathematician Fantasy Land, then Employed Person Fantasy Land, and now my mental vacations take me for runs. Lots of them. Very long. Hilly and flat, hot and cold, rainy and sunny and snowing, dirt trail or asphalt road, I have run in a LOT of locations and conditions without ever leaving my home. Gone to prerace expos and pasta parties and brewery tours. Rushed, panicked, to postrace icy showers, late hotel check-outs and flights home (because in Marathon Fantasy Land, I can afford that, and don’t have to bum a ride from a stranger and then spend the night in a chair in the local state university’s student center, like I did for the Baystate Marathon. I bummed a ride from another stranger back to Boston after the race. All told, that “race weekend” only cost me $2, because during that long-ass night in the student center, I got bored enough to buy a pack of Skittles and a Diet Coke. Fueling plan? What fueling plan?)

Marathon Fantasy Land is not limited to marathons, by the way. I also perform ultrarunning feats in my head. Running across the entire country, east to west. Running up the East Coast from the encouragingly named town of Marathon in the Florida Keys to Halifax, Nova Scotia. Running a Badwater Quad and buckling at Leadville. Doing the Great Cranberry Island 50k in Maine, even though that beautiful race is now sadly discontinued. I’ve heard it’s extremely pleasant to circumnavigate Australia by running. (I have never been to Australia, and there isn’t enough there to make me want to visit it for any purpose other than running its perimeter. So if I ever, ever visit Australia for any reason in my lifetime, I’ll be there for at least a month and I will be running 30+ miles a day. You have been warned.) The East Coast run especially pulls at my heart. I want to do that so badly it hurts. I can’t think about it for more than ten seconds at a time, because thinking about it literally makes me start to tear up. I have planned that run. I need to do it. The minute I find a sponsor, I will be on the next plane to South Florida, bawling like a defrosting Fridge.

Going to Marathon Fantasy Land actually helps my bad left hip and knee joints and my suspected PF on my right foot hurt less. My mind simulates their extreme pain after Mile 16 of a race fairly accurately, but in Marathon Fantasy Land, as in real life, I push through it. I scream in pain with every step if I have to, but I am mentally practicing running despite that pain.

Running a marathon definitely changed me, but not in the way that I’d hoped. It did nothing for my self-esteem, sense of efficacy, work ethic, general pain tolerance, quality of life etc. But it did turn me into a marathoner. It planted a new obsession. I have always been a runner — for over a decade before my first ‘thon, I’d been happily running 5ks, 10ks, and 10-milers — but this is an entirely new level of obsession, not just with running, but with a specific distance. I am in love with the marathon. It is stupidly difficult to keep myself from just going outside one day and running 26.2 miles for my training run – terrible joints, PF, and Boston winter be damned!

I am, of course, in very small part seduced by the idea that during a 50+ mile ultra, the optimal caloric intake is 375 cals per hour, so every two hours during my (for example) suicidal run from Marathon to Halifax, I would be literally required to eat a vegetarian cheeseburger and drink a Shock Top. “But Fridge,” you object, “don’t you hate eating?” Yep, I do. But I hear that during an ultra, after Day Three or so the crew gets tired and relaxes their standards on pretty much everything, adopting an “anything to finish so I can go home” attitude, so they’ll stop caring about whether or not I trade the cheeseburger for three more Shock Tops and run the next seven miles drunk off my ass. I digress.

I need to leave Marathon Fantasy Land very soon, if I want to a) sleep tonight and b) do a massive amount of Responsible Adult things that have been piling up like crazy lately. Hopefully, I will dream about running. Even in my extremely exhausted state, there is nothing I would love more than running for eight hours straight without leaving my bed.

Keep Calm and Mara Thon

On Sunday morning, I will be waking up before sunrise to run 26.2 miles. I paid about a hundred dollars to do this for fun.

…yep, I’m on of those people.

It’s the Baystate Marathon in Lowell, MA, and it will be my first marathon. I’ve been training, and I do have a running base anyways, but I consider myself underprepared both physically and mentally. Nonetheless, I am certain I will finish. I mean, it cost me enough money that I don’t have a choice.

Reading running blogs and listening to running podcasts and reading running books the way I’ve been doing obsessively for the past month or so makes it crystal clear to me how easy it is to get sucked in. Marathons are addictive. Once you’ve run one, you’re funneled by momentum onto the path of running ten, twenty, forty, eighty, et cetera. Once you’ve run your first, you’re certain that your fiftieth will be a piece of cake. A switch is flipped, and you transform from barely-even-able-to-call-yourself-a-real-runner to a Marathoner, someone who can eat 26.2 mile races for breakfast. The marathoning community is very social, active, insular, supportive, intense. These are people who see each other again and again, race after race, because they just can’t get enough. (There’s even an official club for people like this – the Marathon Maniacs.)

Like most questionable addictive habits, however, marathons are expensive. Race fees are always around $100, there is travel and lodging involved, and your running shoes will need a lot of replacing. (Pro tip: good running shoes aren’t cheap!) So the moral of this story is that I’ve got some new motivation to publish the two books that are waiting in the wings. If I can earn just $100/month in royalties from them, that’s funding for a running habit of about three marathons per year!

…wish me luck.

Lexicographic OmNom

Some brand-new words and their definitions:

Insomnomnia – Difficulty falling asleep or staying asleep because you are too busy eating.

Geomnometry – The axiomatic study of the properties of foodstuffs that remain invariant under transformations such as consumption.

Omnomnibus – A large compilation of reprinted cookbooks.

Comnomradery – Spirited dinner companionship.

Comnommunism – The economic philosophy that each person should contribute to the dinner bill according to their means, regardless of who ordered the filet mignion and who merely got a salad.

Somnomnambulance – Eating while sleepwalking.

Omnomnipotence – The power to eat anything.

…suggest your own, anyone?

Campers: On Why They Are Awesome

During my summers, I work at a computer camp called TIC Summer Camp (it stands for Throwing Incendiary Coconuts – no, not really, but that’s what I tell the kids), teaching Java and Python to campers ages 7-15. I already teach during the school year, so why would I spend my entire summer vacation doing yet more teaching? Because campers and students are fundamentally different.

The sole concern of a camper is to have fun.

When I’m teaching school, the students have all sorts of goals and expectations flitting around in their minds. To catch the eye of their crush. To maintain an established social persona. To meet their parents’ academic expectations. To meet their own academic expectations. To get into college, or else. To psych up for their big lacrosse match after school. To take good notes. To use my class to frantically study for the test they’ve got next period. To sprint headlong into adulthood.

But summer camp induces something magical. When a kid goes from being a student to being a camper, his entire mindset changes. His goal is to have fun, period. His expectation is to have fun. He is entitled to have fun. Every action he performs will go towards the goal of having fun. He’s not in school, no longer a slave to the social image he has meticulously groomed for the benefit of his classmates. It matters much less if he gets in trouble, or goofs off, or doesn’t retain information — he is not getting graded, and nothing goes on his “permanent record.” There are no tests he has to ace. There is still, at many camps, pressure to perform, but that comes from mostly intrinsic motivation: the child’s own competitive spirit allowed to flourish outside of the breakneck, cutthroat academic rat race, the camper wanting to perform in a way he can be proud of, the camper wanting to be creative because creativity is fun. There is no massive, life-altering consequence for not performing. The only consequence for not performing is boredom.

And in this glorious environment, I get to teach! The mind of the average camper is so much more receptive than that of the average student! My campers do not dread camp, the way some may dread school, or at least approach school with anxiety and trepidation. They come to camp willingly. They look forward to it every morning and go home every evening grinning. They are completely open to learning everything I have to teach them, because they believe it will be fun. They share my excitement about the material… I don’t have to give them that excitement; they come in with it already.

Do reluctant and difficult campers exist? Of course they do! I’ve definitely worked with my share of campers who cannot sit still, and would rather run around the room or play games or goof off than learn programming or work on their projects. I’ve worked with campers whose fun-having style is to antagonize the authority figure (me) in every effective way they can discover. But on some level, every camper realizes that I’m not just another teacher, parent, adult. They are at a Fun-Having Facility, and I am their designated Fun-Having Guide. On some level, every camper is at least open to the possibility that I might have some fun to offer them. That I might, in fact, be able to teach them how to have fun more effectively. Even if I have to spend the entire camp session corralling and wrangling a particular camper, telling him over and over again that what he’s doing is not the best idea, begging and pleading with him to sit down and write some code, at the end of the session, to my amazement, he still reports having enjoyed his experience, reports liking me, and wants to come back next summer and have me as his counselor again. If you’re a teacher, and you can’t convince a student to study and pay attention and learn, you haven’t done your job. But as a camp counselor, even if there’s nothing you can do to control the behavior of a hyperactive and disinterested camper, that inevitable grin on his face at the end of the day still says “Thank you. You are a positive influence in my life. I may not remember how to write a ‘for each’ loop, but I will remember to associate programming… with you… with fun.”

This is why I love camp. And this is why I will happily allow campers to do anything they want to my face with a marker.

campers

A Geometric Perspective On Your Differential Equation, Part 1

While waiting for my eggs to hard-boil, I thought I’d introduce my readers (all \frac{17}{8} of you) to the dangerously delightful world of Algebrential GeomAppliedMathFunctionalAnaletry. I say dangerously delightful because, due to the extremely broad thinking required, very few people do math this way. Don’t say I didn’t warn you.

Say you have a simple algebraic equation, like y = 17x^2 - 8x. Its solutions trace out a locus in \mathbb{R}^2, do they not? So we can visualize an equation, a sentence of numbers, functions, and variables, by thinking of the locus of its solutions in \mathbb{R}^n — its graph with respect to some coordinate axes.

Meditate on this for a moment. I want you to really, really hardcore appreciate that we have a way of visualizing algebraic equations that’s so simple we can teach it to middle schoolers. Stop taking this power for granted. Sing Hallelujah and praise the name of Descartes!

So now we’ve got our example-gadget, y = 17x^2 - 8x, and we want to graph it. All we need is a basis. I choose… \{ e^{int}, n \in \mathbb{Z} \}! I’ve pulled the old switcheroo: we’re no longer in \mathbb{R}^2, we’re in L^2; y is now some kind of forcing function; and our solutions x, while still points in the space, are now solutions x(t)! Who saw that coming?

Don’t be daunted by the prospect of graphing something in an infinite-dimensional space. If you’re graphing any equation as a line, and then you add k more dimensions to your space, your graph merely becomes a k-dimensional surface rather than a line. Just as we think of x the point as a list of coefficients for the i, j, k, etc. basis vectors of \mathbb{R}^n (the point’s “coordinates”), we will think of a function x(t) as a list of its Fourier coefficients. These lists will tell us how far apart two functions are, to give us a sense of geometry. It doesn’t matter that it’s a function space – you can still draw stuff in it.

Now, there are some operators we can apply to algebraic equations. Only usually we don’t call them operators; we call them functions. Things like sine, cosine, ln, exp, et cetera. The graph of y = \sin(17x^2 - 8x) looks a lot different from the graph of y = 17x^2 - 8x, but is still totally within the realm of drawability. Well, there’s one operator I want to talk about that we actually do call an operator, and that’s the differential operator. The graph of y = \frac{d}{dt} (17x^2 - 8x) = 34x \frac{dx}{dt} - 8\frac{dx}{dt} also looks pretty different from that of y = 17x^2 - 8x. But y’know what? We can think of the graph of a derivative in L^2 the same way as the graph of a derivative in \mathbb{R}^n – we took an equation whose solutions we could graph, we applied an operator to it, and now we have another equation whose solutions we can graph.

To recap: Thanks to our venerated hero René Descartes, we know that an equation traces out a locus of its solutions in some solution space, no matter what that space is, as long as it’s got a basis out of which we can make coordinates.

Continue reading →

Algebra: On Why It Is Hard

Okay, I said I’d be writing only about analysis. But let’s have a little background on why you won’t find any algebra here, shall we?

Throughout school, math has always been simultaneously my favorite subject and my worst subject. I loved math, but math decidedly did not love me. This was primarily due to confusion over the mechanics of binary operations over different sets (\mathbb{N}, \mathbb{Q}, GL(\mathbb{R}), etc.). I could not for the life of me deeply understand the multiplication or addition of matrices or fractions, and only even began to understand subtraction of integers (for Pete’s sake!) once I’d taken calculus and learned to think of subtractions as distances on the real line. (Subtraction of non-integers never gave me any problems. Go figure.) During high school, I voraciously interrogated my older friends about their college math classes, and they, of course, told me only of what they thought I’d find “interesting” and “sufficiently college-math-y” — i.e., abstract and linear algebra, with some algebraic topology. I believed, then, that algebra was the entirety of Real Math (i.e. math-after-calculus). The view of Higher Math afforded by the math competitions I attended, Olympiad problems I looked up, and math camps I (unsuccessfully) applied to only reinforced this misconception. I dutifully bought a few abstract algebra textbooks, and enrolled in an online university linear algebra course during my senior year of high school, which I failed spectacularly.  Resigned to being irreparably Too Bad At Math to become a mathematician, I decided to study biopsychology in college, with an eye towards a career in neuroscience. I double majored in math because, masochistically, I was too in love to give it up just yet.

Then, the first semester of my freshman year, I got inexplicably, improbably lucky. What I thought was a routine item of homework given to me by my adviser turned out to be an open problem, and I had solved it. I had actually settled a much more general case than the stated problem, which I later discovered that convex geometers had considered too intractable to even mention. I was starting research in a neuroscience lab at the time as well – the math and psych departments were conducting a holy war for the rights to my seemingly-boundless-though-wildly-inefficient enthusiasm for research – but getting a major result in math convinced me to at least try to pursue a career as a mathematician. By the end of the year, I had dropped the biopsych major to focus entirely on math.

Doing this, as predicted, turned out to be absolute torture. In the spring of my freshman year, I took Math 52, the University of Vermont’s intro discrete course. Math 52 and I got along so poorly that within a couple weeks I dropped the course, and in order to gain the technical right to do so, switched my major from Pure to Applied. This meant that I needed to get a special override whenever I wanted to take an analysis course. The following semester, I took Math 251, Algebra I (Groups), and I honestly do not know how I am still alive to tell the tale. I barely scraped a C-. I never took Algebra II (Rings and Fields). I still couldn’t define an “ideal” if called to.

There are a few reasons, I think, why I find algebra so difficult. In no particular order:

1) Algebra is very jargon-intensive. And not intuitive jargon that you can picture, like “continuous” or “complete” or “converges.” No, jargon like “proper,” “regular,” normal,” “principal,” even “algebra” as a (pluralizable!) noun — words that have completely nonequivalent definitions depending on the specific class of mathematical objects they are applied to. When my colleagues attempt to discuss algebra with me (because I am in the masochistic habit of asking, “What did you learn in your classes today?” “Ooooh, you just finished your homework? Tell me about it!”), I have to stop and ask the definition of every word that isn’t “assume”, “prove”, “that”, “is”, “a”, or “of”. I must then ask the definition of most of the terms contained in the definition. A two-sentence problem expands into several pages of definitions. And this is precisely how I was taught to solve undergraduate algebra problems: “Unpack” each word in the problem; write down each definition; if the solution doesn’t become obvious once you’ve done this, you’re stupid.

2) Algebra is highly nonvisual. I adore Joseph Gallian’s undergrad abstract algebra textbook; I hate Dummit & Foote. Why? Gallian motivates the introduction of each new structure with a real-world application, and Gallian contains pictures. I am a very, very visual learner. If I can’t see it, touch it, picture myself physically manipulating it, then I’m not going to understand it. And abstract algebra is, well… abstract.

Once upon a time, I was visiting friends at the University of Chicago, and sitting in their math lounge with two UChicago math majors I’d just met. They were discussing their research, which was in algebraic… something. I was eating a bag of Skittles and being frustrated at my inability to understand what they were talking about. Finally, I pleaded, “show me that in Skittles!” and emptied my bag onto the table. I was hoping that maybe, if the group elements could be Skittles, they could be arranged in such a way that I could see on the table in front of me some of the subtleties of their interactions. One of the students swept all the Skittles but one to the side, picked up the singleton Skittle, and  emphatically put it back down in front of me. “Bam! Trivial subgroup!” he exclaimed. They laughed.

I can see functions. I can see continua. I can see myself tracing my objects of study in a sandbox, and can deeply understand that if you try to count the grains of sand, or study the relationship between one particular grain and its neighbor, you’re doing it wrong. Lines and curves and measures and derivatives and integrals in the sand are necessary and natural. And indeed, we all live in a (disputably four-dimensional) sandbox. What meteorologist has time to count individual air molecules? What student draws a line on paper by consciously stippling an uncountable number of points? Can you imagine living in a world where time progressed in any way that could not be described as a flow? (What’s that? You say you can’t? Oh good, I have company.)

A piece of wood, a piece of brick, a piece of metal – any hunk of material you could hold in your hands in also continuous. Sure, there’s one of it, but you don’t count its length, width, height, or mass, do you? Sure, it’s bounded by two-dimensional surfaces, but just like a bounded interval on the real line, it’s still continuous. Cut it into n pieces, and you may have given yourself something to count, but each piece is still continuous.

3) “Proof by obvious.” At least in undergrad algebra, most of the statements you’ll be asked to prove are so obvious that you’ll have no idea how they’re not just tautologies. Right now, I am doggedly working my way through UIC’s undergrad algebra textbook, trying once more to teach myself the material it contains, and I am wrestling with problems such as: “If f: X \to Y and g: Y \to Z are functions, prove that if f and g are injections, then f \circ g is an injection.” As a former high school debate team member, I ask: How do you argue something if you can’t even see any points your opponent might use to support his point of view?

If you resonate with this blog post, know that you’re not alone, you’re not bad at math, and you can still become a mathematician! If you can think of any other reasons why algebra is hard, please leave them for me in comments.