Running through my Mind
Zeno's paradox and limits
Tomorrow, I will belatedly celebrate my 26th birthday running the London marathon. As I sit here < 24 hours to the starting line, the nerves are starting to set in, and I find myself ruminating on all the prepwork that went into this that I did and can no longer do.
I’m supposed to be ready I guess — but I only ran my first half marathon race a month and a half ago in Vegas. How did it go? Terrible. But I finished!
Coming from the East Coast, I mistimed my meals, and trust me, it is not fun to be two miles in, needing to number two, and psychologically unable to because the race restrooms are porta potties.
I also upped my mileage over the past few weeks probably a little faster than was healthy for my legs, and so at mile 11, after 12 consecutive weeks of issue-less long runs, I had to capitulate to the pain of my knee caps and the weakness of my ankles. Hobble-jogging the last two miles, I finished! My time was subpar, but I finished.
My coworkers met me at the finish line, congratulated me, asked me how it went, and internally and externally I felt: Terrible, terrible, terrible. But there’s that awkward silence that follows, where the person positively affirming doesn’t know quite how to respond, and forces one to realize, Oh snap, I guess I shouldn’t have said that?
So why the negative nelly? This misaligned perception between Allison the amateur athlete and the spectator is something I’m still in progress of pulling back into focus. I am a woman with a plan — training for the London Marathon, 26.2 miles. 13.1 is only halfway. But hey, I really did 13.1 miles at night on a half-whim, half-plan, and maybe I really should give myself more credit.
The most I had *ever* run in one go as of three-and-a-half months ago (Thanksgiving) was one mile. Yay me. ! Now that number is 20. (In NYC across all of Manhattan into Brooklyn)
Tomorrow that number will be 26.2.
It’s been a game of not stopping — my thinking has been, if I could do one mile, I could do two. If I could do two, I could do four. If I could do four, I could do six. Six, eight - eight, 10 - 10, 12 - 12, 14 - 14, 16. You get the gist. Marathon training via an arithmetic series.
I’ve had so much time to think while on these hours-long runs. A lot of my mental space ends up being filled by deep cut memories elicited from familiar songs or surroundings or observations of passersby. (I wish Jean Marc Vallée was still around to produce more movies that feel like my brain).
One of the memories recently surfaced was that of a lesson from my fourth-grade History of Math camp on Stanford’s campus. I had a brilliant teacher who taught at Menlo School at the time1 , and as part of this History of Math course, she taught us the basics about all the Greek math greats : Aristotle, Archimedes, Pythagoras — and a lesser known Zeno, famous for his paradoxes of motion.
I’ll highlight Zeno’s paradox called the Dichotomy.
“That which is in locomotion must arrive at the half-way stage before it arrives at the goal. — as recounted by Aristotle, Physics VI:9, 239b10
Let’s say I’m running from Union Square (point A) to DUMBO (point B), approximately 5km. Zeno's statement up above makes sense from the perspective where in order to cross 5km, I need to first cross 2.5km, then the next 1.25km, then the next 0.6km. Sounds kind of similar to how I get through my long runs, doesn’t it?
But on a racetrack of a straight line, I wouldn’t ever hit the finish line, if Zeno’s paradox were true, as the distance is broken down over an infinite series. “The runner will not reach the final goal because there is too far to run,” as the Internet Encyclopedia of Philosophy explains. I could reach 4.999km and there’s still 0.001km to go.
Putting this in the context of my marathon journey, I’ve realized my mindbending methodology is probably not the most sustainable way of training, even if it’s gotten me this far. I’m constantly starting too fast and then finish my splits in spurts to hit each moving target, picking out landmarks along the way. 34th Street, 42nd Street, 51st Street, like each of the stops on the MTA. Where my legs can’t keep up, the distance is something I’ve found compressible through sheer mental will — but that’s generally meant the famed runners’ high still eludes me as my brain is chasing the number rather than the journey.
As I’ve gone through my last month of training before the London race, I’ve found it harder and harder to stick with the plan, compromising on the shorter runs scheduled for throughout the week. Unsurprisingly, James Clear is pretty right here: “You do not rise to the level of your goals. You fall to the level of your systems.” And I’ve felt my systems overloaded by the fixation on the achievement that comes with the long runs.
Like Zeno’s paradox, in focusing so much on distance distance distance (goals!), it feels like I’ll never reach the finity of the finish line when there’s always just a bit more room to run in trying to beat my existing records.
I’ve been desensitized to the accomplishment of a half marathon and feel that it went terribly because I didn’t reach the marks for time. The thing about all the intermediary goals that you set arbitrarily within the big one is that while you’re hitting them, it starts to feel like the limit does not exist. If I reach a goal of going so far, then the new goal becomes to go further, faster. If I can do 20 miles, what difference does an extra 2 make? When I have to do 26 miles, am I going to feel the same way about the gap to 30?
The reality is, my body *does* have limits — and in less than 6 months, I know that I have already transcended what I thought I could do. I never thought of myself a distance runner, I had always been a sprinter. And I should probably be kinder to myself. I should try to enjoy the journey more. So I’ll concede by looking at the 4.5+ hours it’ll take me to run tomorrow’s marathon as an episode of pride in how far I’ve come already — and grateful that I’ve been able to do it, thus far, relatively injury free.
It’s pretty crazy that I just woke up one day, decided to do a marathon, and now can.
This teacher might’ve mentioned she had a nephew named Kevin who played for the Seattle Supersonics? This was around 2007 which would mean the Kevin would have to be Kevin Durant. …