Back in July, I entered the final week of the 500 Mile challenge with … er, well, more miles than I’ve got right now. I’m sitting on 291. I hope to knock out 100 this weekend, which will leave four days at 25 miles per day, plus the extra 9 somewhere, to knock out the rest.
Basically, I spent my entire MLK-day break doing math homework. Literally. Every single day, I spent between six and fourteen hours doing math.
It so happens that I rather like math, but I had forgotten how difficult forms that require a lot of manual copying can be for me. We’re working with matrices, learning to do a nifty series of operations known as Guass-Jordan elimination to yield the reduced row echelon form (yes, I am bike-nerdy enough that some part of me went, “OMG echelon YAY! Look, it looks just like a paceline in a crosswind!”).
This basically means that you translate a system of equations into a matrix — imagine a table in which each coefficient takes up one space, with each system forming a row. The coefficients line up in vertical columns; zeroes fill in as needed. A system like this:
x + 2y + 3z = 5
5x + z = 7
…yields a matrix (in this case, an augmented matrix) like this:
| 1 2 3 | 5 |
| 5 0 1 | 7 |
Except imagine that it’s enclosed in a sort of table, which is how they’re normally presented so we don’t go bug-eyed.
Anyway, when you perform Gauss-Jordan Elimination on paper, you basically copy your matrices over and over and over and over as you perform each row operation until you wind up with rref, which looks something like this:
| 1 0 0 | 1 |
| 0 1 2 | 3 |
(By the way, this is not the correct rref for the matrix above; I just plucked the numbers out of the air.)
I could explain the significance, but this is starting to look dangerously like a math blog, and someone else on the internet has indubitably already explained it better than I will.Anyway, so here’s the rub: I like math and I’m actually pretty good at understanding it — but my executive function difficulties make copying anything a functional crap shoot, and copying over and over again … well.
Suffice it to say I’d work through a given problem in fifteen or twenty minutes only to discover upon entering my answers on the MyMathLab website that I’d made some horrible copying error somewhere and totally hosed up my calculations. All the steps would be done correctly, and I’d still get the answer wrong and Have. To. Start. All. Over.
There were problems that I had to work ten times — using the same set of steps each time — before I managed an error-free copy. Ten times fifteen minutes is one hundred fifty minutes – two hours and thirty minutes. For one measly problem.Each set that I had to work through involved seventeen problems. A few in each set were quick and easy, but most weren’t — or, rather, most would be easy if my copying and data-checking skills were anywhere near as good as my ability to grasp mathematical concepts.
I was, at one point, so frustrated that my options were burn the house down or cry. Crying seemed like the better plan. I cannot remember the last time that raw frustration brought me to tears, and in fact it’s possible that this is the first time it has ever happened (in part because my usual response to frustration, in the absence of the possibility of hopping on a bike and pedaling off in a fit of fury, is to stuff it until I explode — I’m working on this).
Thank G-d for Denis, who’s a math geek and was able to check over my work. After a while, we took to sitting side-by-side so he could check every single iteration of every single matrix for copy errors. That was still slow, but it was a lot faster than my previous approach.
Anyway, short story long, I lost a good four days to this process in a weekend. I lost another day to working the finances: I’d promised to do that before I got back to racking up the miles. Now I’m making up for it.
As a result of this process, I’ve realized three things.
First, riding 209 miles in seven days in January no longer strikes me as outlandish in the least. It doesn’t seem like an unattainable goal. This leaves me feeling pretty confident about this year’s training and racing goals (which are, admittedly, still a bit vague, since my schedule of races and big rides keeps running smack-dab into things like our first anniversary and Denis’ birthday, though thus far Denis has not complained about that).
Second, the same copying problem that plagued me in the early years of elementary school is still with me (throughout first, second, and third grade, during which much of our work was copied from . I now understand that it’s a small part of a much bigger problem, but it’s a part I’m currently not sure how to deal with. Today I got three awesome erasable gel pens (they actually erase quite well, unlike other erasable pens I’ve tried). I’m hoping that using blue ink for positive numbers and red for negatives might help me avoid one of my most common copying errors, which is simply forgetting to copy over the negative sign.
I’m using blue for positives instead of black or pencil to make them stand out more brightly against the graph paper I’m using, and I’ve also ordered some graph paper with larger squares — half-inch rule instead of the usual quarter-inch, which I suspect will help considerably, since it will allow me to write in a larger hand.
Third, I am really happy that somebody invented graphing calculators. My math professor told us to practice reducing small matrices — two by three and three by three — by hand; larger ones require more steps, which make copying errors more likely. Once I realized it was probably okay to do those ones with my trusty TI-84, since I understand the process just fine, I started using it. That improved my life vastly.
Anyway, I’m planning 50 tomorrow, 50 Sunday. If I’m feeling spunky after 50, I might go for a metric. I should really have done one the last time I had the opportunity to get out on a long ride, since I was only 20 miles short when I got home.
“Only twenty miles short” is a strange thing to say still. It wasn’t so very long ago, less than three years, that a twenty-four mile ride was a reason to really celebrate. I’m hoping this year I’ll be able to push that out a little more.