PRIME WALKING

I knew a few mathematicians when I was at university.  They were wonderfully strange and generally not very happy people, though I hardly knew a representative sample.  The mathematics faculty was notorious for being a sort of playroom: very serious people sitting around staring into space or playing three-dimensional chess, and then one of them would say “Ah, I’ve had a thought about the scaling limits of critical Ising correlation functions in planar domains,” then get up and jot down a few equations and this would be a good day’s work.  In some cases it might be a good year’s work.  The whole place looks like a funhouse these days:

I never met a mathematician who was much of a walker, but now thanks to an article in the New Yorker, by Alec Wilkinson, I know about Yitang Zhang – a Chinese-born American mathematician who’s done some genius-level work on prime number theory, who is also something of a walker.

Although Zhang was thoroughly trained as a mathematician, with a PhD from Purdue, he nevertheless spent many years outside of academia, doing various bum jobs: delivery man for a New York restaurant, working in a motel in Kentucky, and in a Subway sandwich shop, before doing his great work, formalized in a paper titled “Bounded Gaps Between Primes” which won him a bunch of prizes including a MacArthur “genius” grant and enabling him to become a professor at the University of New Hampshire.

In the New Yorker article Wilkinson asked Zhang if he was ever frustrated in those “missing” years. and he replied, “I was tired.  But many times I just feel peaceful. I like to walk and think. This is my way. My wife would see me and say, ‘What are you doing?’ I said, ‘I’m working, I’m thinking.’ She didn’t understand.”

Wilkinson also tells us about Zhang’s current situation, “Outside his office is a long corridor that he likes to walk up and down. Otherwise, he walks outside.” You can see why he might stick with a tried and trusted method since his great mathematical breakthrough came while he was walking.

He was visiting his friend Jacob Chi, a music professor, in Pueblo, Colorado, a visit on which he taught Chi’s son calculus.  Wilkinson writes, “Zhang had planned a break from work in Colorado, and hadn’t brought any notes with him. On July 3rd, he was walking around the Chis’ back yard. ‘We live in the mountains, and the deer come out, and he was smoking a cigarette and watching for the deer,’ Chi said. ‘No deer came,’ Zhang said. ‘Just walking and thinking, this is my way.’ For about half an hour, he walked around at a loss.”

And then came the breakthrough, a theorem that proves there are an infinite number of prime pairs that differ by some number N, and that N is less than 70 million.  I think that’s the deal, anyway.

There is a documentary about Zhang by George Csicsery titled Counting From Infinity which shows Zhang walking, and to be fair sometimes not walking.

Of course, Zhang’s is a great story because it’s about a genius who spent a some time in the wilderness and then returned in triumph.  From what I know of mathematicians, quite a few of them walk in the opposite direction.

UNDER THE PAVING STONES, MORE PAVING STONES

Two quotations for your consideration (as Mr. Rod Serling might say):

ONE: “If I do not walk I cannot make a work of art.  The physical involvement of walking creates a receptiveness to the landscape. I walk on the land to be woven into nature. A road walk can transform the everyday world and give a heightened sense of human history.”  Hamish Fulton.  That's him below, and yes, that's a map of Paris - stay with me on this.

TWO: “Under the paving-stones, the beach!” which is the translation of a graffito seen on the streets of Paris in May 1968, and I suppose for some time after that.  I wonder when they cleaned it off.  It also happens to be the epigraph of Pynchon’s Inherent Vice.

Frankly I’ve never been very sure I understand all the nuances of what “sous les pavés, la plage” really means, and perhaps that very ambiguity is the reason it’s had such wide currency, why it’s become such a hit.

Certainly we all know that some of the paving stones of Paris were dug up and thrown during the events of 1968, but as images from the time show, there was no beach beneath them, which of course we all knew anyway.  Paris – believe it or  not - was not built on a beach.

The slogan does fit a little better with Pynchon’s novel set in the fictional Gordita Beach which bears a striking similarity to Manhattan Beach, just 2O miles down the road from Hollywood, and where Pynchon lived in the late sixties and early seventies while writing Gravity’s Rainbow.  I’ve walked there and it’s a good place to walk but I think very few, if any, early-career novelists can afford to live there these days.

As for the Fulton quotation, well, after you’ve read and thought about Hamish Fulton’s heroic walking activities, any walk you’re likely to do in your own daily life is likely to seem a bit trivial and timid.  At the weekend, for instance, the Loved One and I were in Yucca Valley, and we went up to Landers, driving, walking, poking around in ruins, including a walk partly up and partly around Goat Mountain.

Walking and poking around is what I do (it may even be my “art”) – but I’m always aware that certain walkers would turn it into something more thoroughly programmatic - maybe ten circular walks around Goat Mountain at different times of the day, at different phases of the moon, stopping and taking a photograph or picking up a rock every hundred yards.  Well, why not?

And something that occurred to me while I was in Landers: I like walking in cities and I like walking in “nature” but I actually think I may have done the majority of my walking in suburbs.  Now, I think that suburbia is surprisingly hard to define, but I know it when I see it, and I’ve seen plenty of it.  I grew up in various suburbs in Sheffield.  Vast swathes of London, where I lived for a long time, are by any measure suburban, and Los Angeles where I live now is, by many accounts, the most suburban city in the world.  You might think I’m attracted to suburbia.

And it so happened that the motel where we were staying in Yucca Valley was right next to a thoroughly suburban subdivision.  My knowledge of Yucca Valley is patchy, but as I remember it this suburbia scarcely existed even ten years ago: it was just naked desert.

And so these suburban bungalows and ranch houses have descended on the desert like alien presences.  I can’t say I found it especially horrible (though it would surely have been better left untouched), and as I walked around the sidewalk-free streets there was always something interesting to look at, some interesting architectural features, some quirky gardens, and what you see in most cases is a willingness to let the desert show through – to celebrate the desert, within the confines of a domestic plot.

Some of this, admittedly, seems less than authentic. I did see a few garden-bound saguaro cacti, and I think no saguaro ever got to Yucca Valley except on the back of a truck. 

The gardens with Joshua trees seemed a little more “natural” but even here I couldn’t shake the feeling that some of the trees had been, at least, moved around and transplanted for the sake of the picturesque (see John Ruskin, op cit).  The presence of desert quail and jackrabbits was far more convincing.

At the time I was walking, early morning, people were leaving home and going to work – some in very clean trucks, some in surprisingly fancy cars, and one or two of them seemed to slow down to take a good look at me to see if I was up to no good, but maybe that was just my paranoia: an honest enough Pynchonian trait.

Would I like to live in a desert suburbia?  Well no, not much, since in the case of Yucca Valley there’s no adjacent “urbia” where I could go to get my city-boy thrills.  The desert fantasy is to own 100 acres of sand and scrub, big enough that a couple of laps of the boundary would constitute a reasonable walking expedition, though I’m sure some would still find that trivial and timid.

On the other hand, I’d quite like to walk a few laps of this place, though I can’t tell you exactly where it is.  The photograph is by Christopher Gielen and is titled (as it were) “UNTITLED XXXI Arizona” from the book Ciphers.

Under the desert, another damn desert.

WALKING IN SUPPORT

I recently became Facebook friends with the “walking artist” Hamish Fulton (actually I’m not sure if those inverted commas are required or not) - that's him above and below.  Anyway, I’m sure this friendship is far more of a thrill for me than it is for him, but as you can see from the photographs, he’s quite an affable chap, and we’ve exchanged a couple of personal messages, which is more than I’ve done with the majority of my Facebook friends.

Fulton has walked all over the world, and some of the walking has been insanely intrepid – 1000 miles in 47 days from Duncansby Head to Land’s End, eight one day walks and a climb to the Summit of Marmalada, a peak in the Italian Dolomites, a month long coast to coast walk from Bilbao to Rotterdam.  He makes art works based on the walks, often using text, and these subsequently appear in galleries.

Fulton also sometimes walks with largish groups of people; volunteers who sign up to become part of an art project or performance.  One particularly fine one titled Slowalk (in Support of Ai Weiwei) took place in the Turbine Hall of the Tate Modern in London, a 2 hour walk in which participants made 4 separate half hour walks across the length and the breadth of the hall, a process requiring the walkers to slow down to a snail’s, or a certain kind of human's, meditative pace.

Apparently it’s not always so easy to get volunteers.  In his book Keep Moving he tells a story of being invited to Santa Fe, New Mexico in 2003 to conduct an eleven day group walk, but when he got there he found that not a single person had signed up for it.  He says, “Undeterred, the walks I made were wonderful, and for the first time I made a series of walks all within the ‘limits’ of a city.  I performed seventeen circuits of the same route.”  Good for him.

Fulton also comes up with some pretty good walking quotations.  His website opens up with the line, “An artwork may be purchased but a walk cannot be sold.”  Pick the bones out of that one, art collectors.  Elsewhere he’s said, “The texts are facts for the walker and fiction for everyone else.” “An object cannot compete with an experience,” “Walks are like clouds they come and go.”

In another interview in Keep Moving he proposes another work of art, “The idea is to walk for 1000 miles ... all inside Los Angeles, California.  This means averaging 33 miles a day for about one month … it strikes me as a very strong idea.  Of all the cities in the world, surely LA is the epitome of a car city, of a non–walking city … the 1000 mile city walker would be basically indistinguishable from any other category of person walking for whatever reason.  Any ‘suffering’ that may occur as a consequences of walking for sustained distance on concrete would be offset by the thought of making such a clear comment on our car dependent culture and the ensuing politics of the oil industry ... I’m sure the experience could set in motion a new creativity in my work.  Art dedicated to the Chumash and Gabrieleno Indians.”

         Since the book was published in 2005 I wasn’t sure whether he’d actually done this walk. So, since this is the kind of thing we Facebook friends do, I messaged him and asked. He replied “Hi Geoff, great to hear from you. No, I haven't, but it's still on my list. It will be called the Jay-Walker's Blues. I'll keep you posted.”

I can hardly wait.