Cutting sequences on the double pentagon, explained through dance

This past spring, I spent some time "dancing my PhD." I created a video that explains my PhD thesis through dance. I am really happy with the finished product. Watch it and understand!

 
Cutting Sequences on the Double Pentagon, explained through dance from Diana Davis on Vimeo.

 I created this video to enter in the contest "Dance your PhD," sponsored by Science and TED. The contest closes on October 1, and the winners will be announced thereafter.

No matter what the judges think, I'm really glad that I made this video. It's a great way to explain my PhD work to people; I plan to use it in math talks in the future; and it's spread the word about my research in ways that simply writing papers and giving talks never could. I've received emails from many people I've never met, praising the video. It's been a great experience!

Leave your body on the earth

Three people with dogs are ahead of me. As I pass them, one of the dogs runs to the other side, its leash stretched across the path. I trip over it and go flying across the gravel.

"Are you okay?"
"I'm fine." I am laying on the dirt. I stop my watch. I close my eyes, put my forehead down on my arms, and wait.

"Let me help you up."
"No. Just leave me here. I'm fine."

It's best if, when I leave the earth, my body is on the ground. I wait.



"Are you okay?"

I open my eyes. I'm laying on the ground. The dogs -- the leash -- that's right.

"I'm fine." I get up, assess the damage to my skin, brush the dust off my clothes. We exchange a few more words, then I start my watch and start running again.



That mile is 7:55, but the next two are 9:30 because I am telling myself that I know how I will die.

Some day, as it has happened a hundred times before, something stupid will happen -- I will trip and fall, or bang my knee on a table -- and, knowing what is coming, I will lay down, put my forehead on my arms, and wait. And as it has happened a hundred times before, my breathing will slow down, and my heartbeat will slow down, and that which is me will cease to exist. For how long? I never know -- ask the people who have watched it happen.

And then someone says -- "Are you okay?" And a hundred times, I say, "I'm fine," and I get up. And what if, the hundred and first time, my breathing slows, and slows, and slows, and then ... ?

Also see: vasovagal episodes.

Running vignettes

I think of vignettes as line segments approximating a curve. The curve is your life. The line segments are the stories. They start off of the curve, come in and just barely kiss it, and then veer away from it again. One segment doesn't approximate a curve very well, but if you get a couple of them, you get a good idea of what the life is like.

"The loop starts here, right?" I asked the man who has run with this group for 30 years.
"No." He pointed to a spot 30 feet away. "The loop starts there."

I am running in a park. "Excuse me," a teenage boy says, so I stop. He mutters something breathily, in a thick English accent. "What?" I ask. He breathily mutters the same thing again. I still have no idea what he's saying, but now I know it's something lewd. I start running again. "Sorry, I don't speak British," I shout back over my shoulder.

I passed the same old man twice, on the way out and on the way back. Each time, he stood well off the path, motioning for me to go by. As soon as I was past, he made loud farting sounds with his mouth.

I ran past a man who was feeding the ducks. "Well done!" he shouted, "Well done this morning! That's why we're the best!"
"USA! USA!" I shouted back, and pumped my fist in the air. Just so we're clear on who, exactly, my running is making the best.

I am running along the canal, and a woman in a rowing single is going the same speed, just ahead of me. We travel together for a few minutes at the same speed, until I turn off of the path into the woods. And I wonder, if I had a friend who rowed, could we exercise together like this, her on the water and me on the path, chatting back and forth?

Mile repeats at Iffley Road

Mile repeats are my favorite workout. Unfortunately, I only do them about once a year. Fortunately, today was one of those days.

I am currently in the process of molding my body to the task of running 13.1 miles at 6:00 pace. So I ran six mile repeats with 90 seconds rest, in 6:00 or just under.

Well, that's not quite true. In the middle of repeat #4, I took an unscheduled pit stop. So repeat #4 was more like a 1009m, a several-minute break, and then a 600. Then 90 seconds rest, and back to our regularly scheduled program. I was kind of annoyed about this pit stop, occurring as it did in the middle of an interval, and giving me too much rest. However, it was non-optional. That's just the way it goes sometimes.

On the bright side, I had been really working hard during repeat #4 and was thinking of stopping after 4, but after my excessive rest interval, I felt nice and recovered, so I went ahead and did two more miles and finished the workout.

Previously, the most mile repeats I'd ever done was five, in a workout a few years ago with my friend Melissa. That time, we also did them in just under 6:00 -- but we had more rest, and I think they were 1600s. My workout today was on the Roger Bannister track at Iffley Road. I did miles. To do 1600s would have been disrespectful.

Well, that's not quite true. I once did nine mile repeats. But it was really just a way to break up a 20-mile long run.

I like this idea of "molding my body to a task." I think it's the right way of looking at the goal. So I am working on teaching my body to relax and enjoy hanging out at 6:00 pace. The more time I spend there, the better. Six miles in the books.

Do not fear the rain

Suppose that you are in Providence, and the following sequence of events occurs:

- The sky gets kind of dark.
- The wind starts to blow.
- You feel a few sprinkles of rain.

What should you do?

The answer is: run. Wherever you are going (and you must be outside going somewhere, because you felt a few sprinkles of rain), you should start running, because it is about to start pouring rain.

In Oxford, this is not the case. Several times now, I have been outside and those three things happened, and I thought, "oh no, I'm going to get soaking wet," and then -- nothing. A few sprinkles, and then nothing more.

On the other hand, I was doing a track workout on Wednesday, and during the workout the sun came out, and it was evening, so the horizontal rays of the sun made beautiful colors on the buildings and the track, and it was so bright shining in my eyes that I thought about sunglasses. Then, during my cool down run, it suddenly started pouring rain and I was soaked immediately.

I brought all of this rain gear -- a nice light raincoat, an umbrella, knee-high rubber boots, and full foul weather gear. But the only times I go outside are to run, to go to the grocery store, and to meet with my advisor. I'm not going to wear any of that stuff to run. I'll postpone my grocery trip if it's raining. So I brought all this stuff to England in case it rains while I am walking to my once-weekly meeting with my advisor. Hmmm. Maybe I should start going to the library (but only when it's raining), to have an excuse to wear this stuff.

Run in circles

Today I showed up for "cross country training" with a local running club, the Headington Road Runners. The workout could be basically summarized as: run around a very small loop, then run in a larger loop, then run in an even larger loop, and finally run around the largest possible loop.

I loved it.

Before I went, I wasn't sure what to expect. "Cross country training" -- does that mean that we just do a distance run across a heath? The email said to bring spikes, which I thought was an excellent sign.

First, we did a group warm-up around a small circle. You can see it in the GPS track below (it's the small circle). We jogged, and did butt kicks and high knees, and short sprints, all around this circle. At first I felt a little ridiculous -- it was maybe 20m in diameter -- but then I understood the purpose, which is that everyone can warm up together, regardless of speed.

The tiny loop is the warmup; the heart-shaped is the first set; the large loop is the second.

The time trial was around the whole park, outside this picture.

I just knew this workout would look awesome on the GPS track.

The workout consisted of three 10-minute "efforts." The first was around the heart-shaped loop, which was so designed to make us run uphill twice within a very small loop. We just ran around it continuously for 10 minutes, passing and lapping other runners at will.

Then we rested for 5 minutes. This meant just standing around and listening to instructions for the next effort. The biggest difference from running at home that I have found in both this workout and the track workout I did the other day was the utter lack of non-interval running. Mile warm-up, half-mile cool down, and stand around between intervals. These people clearly do not pad their mileage like I do.

Mile 1-1.5 is the warmup, 2-3 the heart loop, 3-5 the medium loop and 5-6 the time trial loop.

I just knew this workout would look awesome on the elevation graph.

Then we ran around a bigger loop for 10 minutes. Then 5 minutes standing around. Then we did a "time trial" consisting of a loop around the entire park. My time was 9:00 for 1.43 miles (6:18).

It was simple, and I liked it. I ran hard, and I was tired afterwards. It was great cross country training; we ran through thick grass, around tight turns, through marshy spots, under trees, up and downhill, in spikes. I am definitely going back next Saturday.

Negotiating gates

The first week or two that I was running in Oxford, I was very concerned about all the slow running I was doing. Before I left, I ran 82 minutes for the half marathon, and I came over here planning to train some more and then run under 80 minutes in a half marathon. That's about 6:00 pace for 13 miles. However, it was taking a huge amount of effort just to run 8:00 pace. This was a bad sign.

I tried to attribute this slowness to all the gates I had to pass through during my runs. Let me tell you a little about the gates around here. Some of them are normal gates, like a door in the middle of a long fence; you lift the latch, go through and then latch it again. But then they also have these other kinds of gates, which I had never seen before I went to Ireland in February. Here is one:

This (above) is the first gate of this type that I ever saw, at Tara, outside of Dublin. I thought it was so amazing that I took a picture. It effectively lets people through, but prohibits everything else. Also, only one person can go through at a time, so if a bunch of people all want to pass, it takes a while.

Some of the parks here in Oxford have taken this style of gate to a whole new level. Unlike the one in the picture above, these things are like eight feet tall. Good luck passing a bike or baby stroller over them.

In case you do not fully understand how this sort of gate works, here is a top-view diagram I have made for you, showing how you can enter at the bottom, flatten yourself against the wall on the right, and then swing the door across so that you can exit out the top:

This evening I showed up at an OUCH group run, thinking that they would go about 8:30 pace, which is what they did when I showed up to their Tuesday lunch run. Instead, I ended up running with this one 50-ish guy, who ended up being really fast. We averaged just over 7:00 pace, including passing through several gates of the type exhaustively described above. It was amazing. It revolutionized the way I think about gates. Now I think: just open it and move on, preferably at breakneck speed (and preferably with a nice man who darts ahead, opens it, waits for you to go through, and then closes it). Never again can I blame gates for my slow pace.

Cow grates, on the other hand...

Flapjacks

As I mentioned in my previous post about the Witney 10, after the race I purchased and ate a large homemade granola bar. However, said purchase was not without a cultural exchange.

"How much are those?" I asked, pointing towards a plate that contained sugar cookies and large homemade granola bars.

"The flapjacks are 1.50, and the shortbreads are 50p."

Hmmm. In my opinion, the plate contained neither flapjacks nor shortbreads. I figured that the flapjacks were probably the flat things (cookies) and the shortbreads were probably the little loaf things (granola bars).

"Okay, may I have a shortbread?" She reached for a sugar cookie. "Uh, no, one of those." I pointed to the granola bars. "Oh, you want a flapjack."

"Those are called flapjacks?"

And to think that the world's canonical dictionary, the OED, was written by the people who gave these names to baked goods.

Compare and contrast, U.S. vs U.K. road race (Witney 10)

I am getting tired of running by myself all the time, as it is much harder to maintain a good pace by myself than when I am running with someone else. When I saw that there was a 10-mile race nearby on Sunday, I decided to jump in and run it for my long run. Happily, there was a bus that took me to within a half-mile of the race, and it only cost £12 (about $20) to enter.

Things that were the same as road racing in the U.S.:
- I registered, paid, and picked up my bib number
- people warmed up and lined up, the gun went off, and we raced
- the miles were clearly marked, with volunteers at intersections, water stops, and some spectators
- I got a tech T-shirt
- They eventually ran out of smalls and mediums
- prizes were awarded for top finishers in various categories

A sign I saw as I was barreling down a hill midway though the race

(I did not take this picture, but the sign was just like this one.)

Things that were different from road racing in the U.S.:

- T-shirts were for finishers, not entrants: you got one just after finishing the race, next to the water table

- There were no free post-race refreshments! The PTA was selling baked goods, and you had to pay for them. I paid £1.50 ($2.50) for a large homemade granola bar, because I had just run 15 miles and I needed to eat something. I asked another runner about this, and she said she has almost never been to a race that gave out free food afterwards. Note to self: BYOPRP (bring your own post-race picnic).

- The people running were called Men and Ladies

- Women's age categories were Senior Ladies, V35, V45, and V55; men's were Senior Men, V40, V50, V60. Notice how they are not the same. I don't know if that is peculiar to this race, or true in general.

- There was no parking lot ("car park") near the school, so they directed people to use a car park literally about a mile away. We had to walk past the bus stop, through a field, over a river and past a new development of a former blanket factory made into apartments (Witney was once the Blanket Capital of the World), to get to the car park. When the parking is that far away in the U.S., they have a shuttle (or pick a different race HQ that does have parking).

Pretty much everyone in the race was a club runner, wearing either a white singlet with a horizontal yellow and blue stripe, or a yellow singlet with a horizontal navy stripe, etc. for the local running clubs. I took home the first page of the results, and in the top 50 there are only four people who didn't put down a UKA club affiliation -- though some put down a team for which they are the only person, as I did: New Balance Boston. This race doubled as the Oxford 10-mile championship, so at the end of the awards, the top teams received medals.

As for the race itself, it was extremely hilly. There was a warning to this effect on the web site, so I was anticipating a tough, hilly course, but it exceeded my expectations in this regard. I also looked at the course elevation profile, and noticed that it was basically uphill until mile 4 and then downhill thereafter. "Uphill until mile 4" was accurate, but it was not downhill thereafter. It was full of steep little  hills all the way to the end.

Here you can see the very hilly elevation profile from my awesome GPS watch, and my associated fast-beating heart rate, over 180 most of the time:

The other thing about the race that is similar to races in the U.S. is that despite finishing second female (excuse me, "lady"), my prize was less than my entry fee. I paid £12 to enter and I won a £10 gift certificate to the Oxford running store. Now admittedly, I was fortunate to win anything, and if I had entered by mail it would have cost me only £10, so I would have broken even, and also I got a T-shirt, which is worth at least £2. But still, I was a bit surprised by the smallness of the gift certificate.

I believe that in any race, if you place in the top three, then the value of your prize should at least equal your entry fee. I believe that if you win the race, your prize absolutely must at least equal your entry fee.  However, like many races in the U.S., the Witney 10 did not satisfy my rule.

Oh yeah, the actual race. I had some desire to win the race, so I went out right behind the first woman (Sophie) with another woman (Nikki) right behind me. As we started to climb a steep hill, I realized that I was running too hard for a 10-mile race, so I slowed down and Sophie ran away. She would finish 4 minutes ahead of me, so that was the right choice.

Nikki ran on my shoulder until a little before 3 miles, and then fell behind so I couldn't hear her anymore. I glanced back at 5 miles and she was nowhere to be seen. However, around 7-8 miles a spectator said, "Well done ladies, second and third ladies overall," and I was displeased to see that she had caught up to within about 20 meters! Maybe that was because I had been averaging about 6:45 pace. I ran hard down the next hill and looked back at 9 miles and she was far behind, and 30 seconds back at the finish. In the end, it didn't matter for the prizes because she was in the V35 category, but I still prefer to place second rather than third.

The last part of the race was running around a large grass field. It was torturous. The hills throughout the course were also rather tortuous. And the lack of food afterwards was highly torturous. However, I met some nice people after the race, two of whom offered to give me a ride back to Oxford (which I happily accepted), and I found out about a running club in the area, so I can run with them instead of running alone. I am happy to have had this experience of a local road race in England.

News article

How I learned to just open the darn gate and love the towpath

Last February, when I did my whirlwind tour of Bristol, London and Cambridge, my friend took me on a lovely one-hour run along the canal in Cambridge. In my recollection, it was basically a bike path: maybe five feet wide, paved, flat, along the river where lots of people were rowing and sculling. I eagerly awaited getting to Oxford and running along Oxford's equivalent.

While at home in Providence, I looked at the Google satellite view of Oxford. Look at this awesome path along the river! It even looks like it's dirt; perfect for being soft on the legs! I was especially looking for a place where I could bang out 5-10 mile tempo runs, like the bike paths in Rhode Island.

The dirt path(s) along the canal

My first day in Oxford, I headed south and ran to the very part of the canal that you see in the picture above. As you can see, I had a choice: closer to or farther from the water. First, I chose to run along the water. I was running along basically a trampled path in the grass, and it was full of puddles.

After less than a half mile of practicing my long-jump skills, I gave up, went back to the intersection and chose the path further from the water (the one along the trees and the road). This one had fewer puddles, but it had lots of cattle grates! These cattle grates are like eight feet long, with fences on both sides. I was afraid that if I failed to long-jump it completely, I would jam my foot between the slats and break my ankle, so I had to stop and walk across each one. Fine for a regular run; bad for a tempo run.

The next day, I headed north. Look at how nice this looks from the satellite image:

A lovely, scenic dirt path from the satellite view

Again, I was trying to find a long, homogeneous path where I could let the miles flow. From space, this path seems to fit the bill. However, in real life, it has many bridges to cross (steep little bridges so that boats can pass underneath, despite the canal being 10 feet wide), many gates to open and close (so that the cows don't get out), and many locks to run over (which involves darting left and right through these metal things that prevent people from riding bikes through them). Plus, each gate was different, so I had to stop and see how each one worked before I could pass through it. Not bad for a recovery jog, but who wants to stop every third of a mile in a tempo run? Not I.

Then I happened upon some route maps for a local running club, which went north along a different canal. It turns out that two tributaries feed into Oxford; who knew?

This one is taken at the same zoom view level as the others.

You can barely see the canal (to the right of the road), much less the path beside it.

All you can see are the houseboats.

Here, finally, was an uninterrupted path! You have to go past locks, but never over them. It always stays on the same side of the canal, so no bridges to cross. There are people living in houseboats along much of its length, but apparently none of them are grazing cattle. It is narrow at points, but I can deal with that! Yay, I was so excited that I finally found a completely boring path where I can run a predictable pace for every mile!

Today, I went running with an Oxford student. He took me on a loop that went north along the bridge-gate-lock towpath, and then south along the uninterrupted towpath. When we got to gates, he just opened and closed them. No big deal. We ran past cows, and the ruins of a nunnery. The peaceful river flowed gently by, with birds flying and floating along it. Other people were out walking and running.

Perhaps I should just deal with the gates and appreciate the scenery. I'm not doing that many timed tempo runs, anyway.