Weather grey and cold as an English summer, bus station with lots of customers wanting the Gatwick bus and needing to be reassured that the bus is really here and will come after this bus leaves. In fact the Gatwick bus is the one that, all unknowing, I had planned to take, but of course Sheila was impatient, so here I am on the earlier bus.
Licking my wounds after the RAE panel on Friday. The tenor of the meeting was that the mathematicians were basically agreed on sensible procedures, but the RAE team person kept jumping up and telling us that what we proposed was against the rules. By the end of the meeting she only had to raise her eyebrows and Barry beat a hasty retreat from what he had been proposing.
For example, at the start of the meeting, we had declared our interests. It was agreed that our major interests were in our own universities, and we would be precluded from taking any part in the discussion, or even being present (we knew this already). Minor interests: I declared wife at the Open University, kids at Manchester and Glasgow, none in mathematics departments. It was agreed that these would not require any special action. But when we came to discuss the Open University, her over there suddenly said that I would not be allowed to lead the discussion. However, I would not be excluded from the room; I would have to sit there not being able to correct my colleagues on points of fact. I protested that this was stupid and I wanted clearer guidance, but she had nothing positive to say, then or elsewhen in the meeting.
So there is fun ahead. I have a pile of RA2s in my bag, and hope to have at least some time in Montréal to sit in the library and make a start on them. Perhaps if there's an excursion I could skip it. In any event, I hope to have at least some quiet time while I am there.
I never set out on a journey without worries. This time, it is shortage of OHP slides. There is no way I could prepare enough for a whole series before I arrived, and I forgot to bring lots of blanks and pens. (I have only a few that were at home.)
Anyway, we are now rolling, and have just hit the motorway. Typing on a moving coach is even harder than writing, so more later.
Not much of the outside world impinged on me. I saw a truck on a country lane hauling a trailer with what could have been mistaken for Dr Who's Tardis on the back. I started reading Dorothy L. Sayers' biography. Apart from a David Lodge, brought in case of real desperation, I have that and two books of poems (A. E. Housman and assorted sonnets). Plenty of writing to do. Not only my slides, and the ten missing sections of the write-up of my talk, but more about homogeneous coboundaries (I have decided that I should write it all out properly), the RAE papers, the Erdös paper, and so on. I bought an exercise book at W. H. Smith, and some shower gel at Lloyd's.
I have started on homogeneous coboundaries.
I looked out the window and calculated that a 10000 foot mountain on the horizon would subtend about a third of a degree; so I fantasized that the faint smudge on the edge of sight was Greenland. Nearer, there have been few cloud breaks. One of them showed slow metamorphosis of white caps on the sea, like crowds of fishing boats.
I wrote notes for the homogeneous coboundaries, at least in the complete graph case. I had a bit of a shock when the automorphisms of the coefficient group didn't work as I expected, and I had to use the homogeneity to get them to act. I don't think I have got the final version yet. I don't see how far it will extend. The compete bipartite graph should be OK, I think.
Earlier, the seatbelt signs were on, and the cabin crew clearing away the dinner trays, but still the passengers had to be told three times to sit down, the last with some exasperation.
Dinner was not so great: the hot food cold, the cold food much too cold, and identical vegetables with both (masquerading as stir-fried with the chicken, unidentified with the smoked trout).
It has cleared now, but for much of the flight the view outside the window was a total white-out, something I haven't seen at a Jumbo jet's cruising altitude before. It is still far too cloudy below to see anything.
Approaching Montréal: first, dismal marsh with scrubby trees, then dismal marsh with scrubby trees and warehouses, then add some shopping centres -- and then an accidental glance the other side showed the tower of the University and the dome of the Oratory looming through the grey high above. Along an almost subterranean motorway, we came out at the railway yards, now wound about with concrete spaghetti like some sinister spider's cords, then high over some tenements, past a grey convent behind high bars, and finally to the city centre. I found my way to the Metro, and discovered others going the same way. Now I've checked in at the residences and found my way to the Cote des Neiges, where the Vietnamese restaurants seem to be almost exactly the same as last time I was here.
After, I went for supper to a vegetarian restaurant where they weigh your plate and charge you for what you have taken. The food was really good, and I had fresh-squeezed pure apple juice with it. There was a surprisingly good jazz trio (female singer, guitar, and string bass) playing while I ate.
Walking back, I saw a display like those I remember here, the sun sinking into the murk of the western suburbs; there were two screens of cloud, the front one grey, the back one living orange, like flame leaping above the smoke.
Now I am beginning to wilt a bit, but I have had a shower (really good pressure, even on the nineteenth floor!), and will go to bed as soon as my hair is a bit drier.
The church is not exactly as I remember it: lots of modern stained glass and workmanlike concrete pillars and arches; even the murals and Stations have a very modern feel to them.
First day gone; I have done a bit: I did further sorting on coboundaries, and sat in the office and typed it after the lectures before going to eat.
From lunch in the Vietnamese restaurant today: for dessert you could have "Pommes frites avec creme glacée" (or Bananes frites, if you preferred).
This morning woke at 5:30. I worked for a while, writing notes for circulation with my lecture, and then went for a run over Mont Royal. Unfortunately I turned too soon and ended up on the busy road behind the mountain, without a footpath. I missed the road back to the residences as well. Not a great success, but it felt good in parts.
Yesterday, not a lot happened except several emails and a phone conversation with Sheila which seemed to have the effect of making us both miserable: just what I didn't need.
After the lectures, I ran up the mountain again. This time I did get to the top, and thought I would cut it short by coming down the same way; but I missed the turn and ended up going the long way after all. Still, quite a good run. It was very weird until I realised I really was going the other way: nothing seemed to fit, and then it all fell into place. At one point, going downhill I seemed to be as slow as an old guy shuffling along, but I did pass him, and he looked at least quite fit; then I caught and kept pace with someone apparently running quite easily and fast (with his dog on a lead). Many more joggers than last time I was here!
Lunch was a chicken sandwich which turned out to be chicken paste and cheese.
I wrote a sonnet on the way up here. I had read several sonnets in the book, in which romantic poets were bemoaning the difficulty of squeezing their thoughts into 14 lines. I always find 14 lines a vast expanse and hesitate at the thought of trying to fill it, so I wrote a poem saying so:
Wordsworth refers to it as hermit's cell,
nun's convent room, or prison strait and damp,
small lute or pipe to sing, or glow-worm lamp,
or like a murm'ring bee in foxglove bell.
Rosetti calls it ``moment's monument'',
Misers of sound employ it, so says Keats;
and even Shakespeare filled a hundred sheets,
to paint a broader canvas his intent.
But to such sentiments I can't respond.
The emptiness of fourteen lines, the fog
in which I grope, deny such words as these.
My temper leans towards the Japanese,
for whom each syllable falls like a frog
breaking the silence of an ancient pond.
Before I left the jazz, I saw a group (whose name I didn't catch) who had won the festival prize: a guitar, piano, bass and drums quartet who played their own compositions in traditional style with traditional solo slots. After, I walked around and caught Ceux qui marchent debout (whom I had heard recently on the radio, I think on some jazz program) who were great fun: a real marching band, playing nothing they weren't carrying, full of humour and Mingus. Also, while sitting there, wrote a few haiku.
There were two demented people behind me: she would hum a single note loudly along with the music, and he would beat time inaccurately but so vigorously that the whole stand shook.
I will sit for a few minutes in front of the main building, where the sun sinks towards the suburban sprawl and murk, though it is some way from setting yet. (2044, says Psion.)
Two other people watched it too. A carload of kids stopped, but wouldn't wait, and went away again.
The path wound through marshy land with little creeks and lots of common wildflowers (daisies, vetch, bindweed, several umbellifers, and the blue daisy-like flower that is very common here), and rushes in every damp spot. The path led to the bridge, where I was corralled in beside the freeway traffic. Finally, on the island, golf range, indoor tennis, and lots of new housing development along with lots of highrise offices. (The map seems to show half the island undeveloped -- not for long, I'm sure!)
By this stage I needed a toilet, and was at last driven to have lunch in Dunkin' Donuts to use the toilet there. (All the other eating places appeared to be vastly expensive, though they didn't put menus up, so I couldn't tell. I was sorry to pass a tiny "restaurant canadien" in a suburban street on the way from the Metro; but it was closed then.)
Now I will try to find the other side of the island, the aim being to see a wide stretch of the St Lawrence.
Who would believe it, a bridge two kilometers long just for cyclists and rollerbladers (and maybe walkers)? The view was mindblowing -- two kilometers is a wide river, but this is a bridge built at a narrow point; upstream, it widens out much more. And walking gave the amazing view time to penetrate properly into my consciousness.
On the other side, I discovered that there is more, which the bridge doesn't cross: only the much higher Champlain bridge does. But the cycle path seems to go on, so I will follow that.
I'm now sitting on a pile of rocks in beautiful warm sun, in a thicket of wild raspberries. A small furry animal, much bigger than a squirrel, came running through the rocks, and stopped for a long time to look at me. Perhaps he thought I'd feed him.
The bridge itself seemed as if it would also function as a barrier, but I couldn't see any gates. But apparently it is an ice boom. I am not sure what that does.
The Champlain bridge had steadily climbed so that, though I had walked on it to Ile des Soeurs, at this point it was far above my head, having lifted off its pylons onto cantilevers. Clearly the canal builders had expected very big ships. No way up, not that I would have wanted to; the roar of traffic was frightful even at ground level.
The next spit has little but electricity pylons, scrub, and an enormous and noisy gull colony. I also saw a bird, the size and colour of a blackbird, but with a black beak and very striking red and white flashes on its shoulders, which chatters incessantly.
Now I have to take back what I said about shipping. I arrived at Pont Victoria just as the red lights came on and the booms came down, so I watched the old machinery lift the bridge segment high in the air. First a flotilla of yachts came upstream, most of them small enough to fit under Osney bridge with their flags down. Only two boats went the other way: the first a fairly big cruise ship, and the second a big ocean-going container ship, the Mathilde Desgagnes out of Montréal, loaded with containers, trucks, girders and pipeline; not at all the kind of thing you see in Godstow lock!
By the end, there were hundreds if not thousands of cyclists waiting for the bridge to reopen, many of them families.
I am now on Ile Ste Helene, almost under the Cartier bridge. I just have to find my way up. But I'll have a rest first.
No breakfast or lunch today. Yesterday I skipped breakfast and had just soup for lunch. In the evening I had a light vegetarian meal, with Peter, Cheryl, Alice and the Catalans, and then in the night my stomach hurt, which I took to be a good sign of things beginning to solidify. So far today I have been a bit better. Now, as long as I don't collapse with hunger during my lecture ...
Last night I thought for a moment that I could prove that the sufficient condition for Cayley graphs of a group to be isomorphic to R is also necessary. But I was completely mistaken.
Also last night, the campus was invaded by several marching bands and similar outfits, who were drumming, trumpeting, and dancing on the lawns all around the place, while their coaches (from Quebec, Ontario and the northeastern USA) cluttered up the car parks. I suppose there is a competition on. Perhaps they will start drumming during my lecture. They make a fearful racket. The brass band seemed to be practising blowing their lowest notes, making an extraordinary sound.
I only just got back to my room in time. But after getting to sleep at about 11.30, I slept right through until 6, and now only have a very vague grumbling in my gut.
If it's true, it's just in time for the dinner tonight!
The dinner on Wednesday was superb. The woman who runs the gallery and restaurant was interested that I had seen a Hayter exhibition in Oxford. She was unable to find it in the list of his exhibitions, which only went up to 1991. The dinner was several small (but not too small) portions: smoked salmon (they smoke their own, and don't overdo it), sea bass, duck (like I never had duck before), cream-filled swans with fruit, and some strange cheese with soot in the middle. My stomach held up for the dinner, though I only just got home in time.
Thursday was the conference closing party: plenty to eat and drink, a guitar to play, and I was able to eat and play some. I went home early (about ten), but apparently it continued much later.
Then last night, dinner at Gena's apartment, cooked by him (and partly Dominique). I walked over with Peter Neumann. We had a most enjoyable evening, though I was a bit uncomfortable towards the end. The soup was like nothing I ever had before: fennel, apple and a bit of ginger. Then a lovely pate, very good roast lamb, and fresh fruit with sauce anglaise. We were all very tired, and misbehaved a bit, insulting the host and spilling wine on the table; but we continued in good spirits until 2am.
In the meantime, I have been missing breakfast and lunch and spending all my spare time on the toilet or sleeping. (On Thursday and Friday, I went to my room at lunchtime. The first time, if I hadn't set the alarm, I would have missed the afternoon's lectures: I was very far under when it went off.) Nobody seems to have noticed anything amiss; in fact, yesterday morning after the party Gert remarked that I was looking better than most people.
So what has been achieved here? My lectures went well, and were very well received. Fortunately there were good blackboards. (I am not looking forward to next week.) In each lecture I put a slide up on the OHP and left it there for people to assimilate or refer back to while I lectured. Seemed to work. The stuff on infinite antipodal distance-transitive graphs seems to be sorted, as far as it has gone. I answered some questions from the Cayley graph people (Ted Dobson and Joy Morris). And I have started thinking a little about the compact graphs that Chris defined in his talk. As well, I have met Gena, someone with whom I instantly had a very good rapport (though I expect that everyone does).
Otherwise, I have had a bout of diarrhoea which has gone on for a week, shows no sign of finally clearing up, and has disrupted my life to a large extent. (That said, I just went to the toilet, and things do seem a bit more hopeful.) I haven't made a start on the research assessment papers. And I am if anything more tired than when I came. Progress?
I walked into town, and found lots of street markets, but nothing worth buying. Eventually, after some trouble, I found a bookshop with English language books, and bought the new Carlos Castaneda as well as (for light relief) The Englishman who went up a hill and came down a mountain. Then I went back and got the bus to Mirabel.
I was there before 3, and the check-in didn't open until 6, so I actually finished the Englishman already. I thought of throwing it away, but will take it home --- someone might read it. (There I go again, more pointless self-sacrifice.) After I finished, the queue was starting to form, so I joined it, checked in (through to Pisa), and then went up and had a snack, which I have just finished. At least I seem to have my appetite back!
There is no misfit:
Jethro Tull and Fleetwood Mac,
clouds spread out below.
The sparrows have fled
with the crumbs: comes a lone gull
with unwinking eye.
the cross on the mountaintop,
a weapon, primed, aimed.
See the gatekeeper,
Notre Dame Cemetery,
tending his garden.
rose and shamrock -- the many
souls of Montréal.
Vast plains lie empty;
people in obscure T-shirts
teem in the cities.
From the terrace band,
a trumpet hangs in the air
thick with city noise.
A wayward balloon
soars, swoops, falls from sight. Again
the gulls rule the sky.
A single teardrop
cuts the ice on the window
above English clouds.
I am pleased to report that Britain is a far more civilised country than the USA, as measured by their treatment of transit passengers. You just follow signs for flight transfers; you come to a bus, take it, it goes to somewhere else, you follow more signs for flight transfers, go through a security check, and you are in a departure lounge far more pleasant than the regular one! Thomas Cook have a rest room with showers, internet terminals, the works. (I was tempted but made do with the public toilets to change my underwear.)
I didn't even start on Castaneda; I reckoned that re-reading the Sayers biography would be less demanding. Neither did I think about compact graphs or anything else. At the moment I don't feel too bad at all, just a trace of that heaviness above the eyes.
There is a very fine room-dividing aquarium in the lounge, which has some very fierce-looking fishes along with the plain ones. It is fascinating to watch their gestures; they know whether to ignore another fish or to move out of its way. They appear to be floating in the lounge full of passengers.
There is also a whisky shop which is doing a special offer of a cask of Bushmills (at least 250 bottles) for 4700 pounds for the millennium.
Nasty moment there. I noticed the woman next to me reading a guidebook of Prague. Given that the plane next to ours on the screen was going there, when I dashed out of the lounge so fast, and given the cursory check they gave my boarding pass, it was quite possible I was on the wrong plane! Then I remembered the pilot describing the view of Lake Geneva and Mont Blanc, and relaxed. Perhaps she is on the wrong flight.
Alex and his student duly arrived. There was a driver from the conference centre to meet us, and we persuaded him to take us to the Leaning Tower (something the other participants didn't manage, apparently). He stopped for five minutes while we looked at it and Alex bought some souvenirs. Then up the mountains, past rock faces and olive groves, looking down on an Italian plain with red tiled roofs and blue distances.
Through a tunnel, we were in a different and much greener world. The road here goes up a big valley, then up a much smaller valley where it always seems that it is going to end in a sheer mountain wall, and then finally a point where the valley widens out, ringed by serious mountains with quite a jagged skyline. From the terrace of the conference centre one sees over the whole plain, with the town of Barga on a small hill up the valley a bit.
Very hectic schedule. Only 1 hr 40 mins for lunch, no siesta. This afternoon Zelmanov talks for 2 hours.
I haven't yet explored the swimming pool or fitness centre, but I found my way to the shop by following Ian Chiswell. They undercut the bar by a large factor. (I was a bit amazed that nobody seemed to be having a pre-prandial drink last night, until it was explained to me that beer is 6 pounds per pint.)
I discovered when I re-read my abstract that the topics on my slides form a selection almost disjoint from the ones in the abstract. I think I will put in one extra topic, and probably not have enough time for it!
I had a longish talk with Alex Zalesski last night. He is keen to set up a rotating seminar on permutation groups under the LMS scheme, which would be very nice. He is talking of recruiting Cambridge and Leicester, which would not have been my most obvious choices.
This morning, there was one pocket-handkerchief sized patch of mist on the edge of the mountains across the valley.
Got through to Dan this morning. He will drive up here at the end of the meeting on Thursday.
It is now completely still and completely hazy.
The floor with the main lecture room also has a terrible smell today. It is so still that opening the window doesn't help.
I meant to have a rest before dinner, but they are still cleaning my room.
The hills at the far end of the valley are already hazy, but the ones opposite the hotel are still fairly clear, and make a lovely backdrop to the pines and poplars round the swimming pool. The two big mountains are much whiter (exposed rock rather than snow, I think).
The footballers seemed to be leaving this morning. They were great mobile phone users, especially the manager, who (according to various people) spent a lot of time arguing about the number of millions of pounds in a transfer fee.
One tiny village, whose lights at night form an arrowhead pointing at the sky, is balanced on top of an impressive hill commanding a subsidiary valley. The ground in front of it has been cleared and shows up lighter, as if the village and its surroundings are spotlighted by the sun.
It is such a pity that the timetable allows no time to explore the country around. (Though many of the sheer slopes would be inaccessible to non-climbers.)
Near at hand, on the terrace, is a pot of geraniums and marigolds, and a palm tree in a huge terracotta pot. Pools of water remain from where the stones were washed down (though not thoroughly enough to get rid of the cigarette butts); they are almost visibly drying out in the warm morning sun coming over my left shoulder.
A coach toils its was up the road (presumably to collect the footballers).
A plane crosses the sky somewhere, and I feel the sound deep in my gut.
It was so hazy at lunchtime that it looked from indoors as if rain was coming; but it's not so.
Nice question from Aner Shalev and Laci Pyber. Is there an absolute constant c such that, if a (finite) primitive permutation group has d generators, then its point stabiliser has at most d+c generators? Sounds outrageous at first, but seems likely to be true (and provable from O'Nan--Scott, Aschbacher, etc. plus a fair amount of work.)
I tried to express what happened in seventeen syllables, to help recall it. This is the closest I came:
With the first sunbeamBut what was it that I understood? In words, something to the effect that death was not a final all-or-nothing process but something that happens continually, and that it is an experience to be learned from.
I broke through to clarity
in the pine forest.
This morning it is even hazier. The end of the valley is scarcely visible, and the white mountain practically blends with the sky.
He arrived a bit early, and sat in on the end of John Wilson's lecture. Then, after goodbyes (and after I'd fetched my hat, which I'd left in my room), we were off.
Dan had found in the guidebook a very nice-sounding restaurant in Bagni de Lucca (which actually turned out to be up a narrow winding road in the hills above Bagni de Lucca). But when we got there, a sign told us it was closed until 8. So we drove back to town and found a perfectly acceptable restaurant for lunch. Then we drove to his farmhouse, a longer drive than I like, especially with lunatic lorry drivers changing lanes without warning.
The farmhouse is on a little hill down a gravel track not far outside the village. After unloading and having a drink, we went for a walk around the farm, with views of the harvested wheatfields and villa-crowned hills with long vistas beyond, and the olives, honeysuckle, and fennel richly perfuming the air. Beautiful. After a while, a light shower came over, huge drops of warm rain, and then stopped, and the sky was full of light-fringed clouds.
We drove to the supermarket to get some Parmesan, milk for breakfast, and a few strawberries. Then we went out to dinner. The village festival was under way, so we ate in the meal tent, where Dan's cleaning lady's brother-in-law, the village butcher, was cooking the steaks. Very nice. Then ice-cream and home. There was absolutely nothing to see at the fair apart from the remarkable cross-section of people, young and old, in the meal tent.
Breakfast: toast with olive oil and garlic, espresso with brandy, and a cup of lapsang souchong. (And cool spring water, and the farmhouse roofs and rounded hills out the window.)
Yesterday I didn't say about the nearness of the earth in that little lane, the reality of its smell and feel and the amazing rain.
Cypress trees, like flames,
lick the hills of ancient stone
circled with olives.
Before the heat haze
the mountains are blue curtains
behind the pine trees.
wheat straw, olive leaves, red tiles,
dark tree silhouettes.
There was an airport check-in at the station, so Ian and I got rid of our bags, had a beer, and caught the train. We decided, since we were in plenty of time, to get off at Pisa Centrale and see the leaning tower. We bought a map and found our way there on foot, then walked round the duomo looking at the fine carvings and mosaics and catching the tower from various angles. Then we caught the bus back to the station. (A woman at the bus stop sent us to the newsagent for tickets, he sent us on to a bar, but that worked.) Then we took the train to the airport and checked in.
The plane was loaded and ready to go early, but air traffic control kept us waiting for forty minutes. This is an obvious absurdity, since Pisa has only about a dozen flights a day, but the pilot said it is all done from Brussels (which doesn't give me confidence). After we took off, we circled low over the city, getting yet another view of the cathedral and the tower.
Now over the sea, with delicate cloud shadows on the water. Level fields of fluffy clouds with occasional dramatic eruptions. The background to all this is an amazing misty grey full of light. Above, cirrus tails hurry by in the deep blue.
As well, the French farmlands are indescribably beautiful; a bit like marquetry in many earth shades and greens, but following the contour of the land.
It would have been interesting to see if there were any interesting effects around the plane's shadow on the other side.
A huge estuary, and we are over the sea. It is interesting to see how much less perfect a mirror the sea is: just a sheen over a huge wrinkled rippled area, while the cloud reflection continues. Like the Med, the Channel supports weird fractal cloud shadows, contrasting with its corduroy-like surface texture.
And there's England.
I wrote a sonnet on the bus, typed it at Heathrow, polished it on the plane. It still needs more polishing.
Window seat on the plane, sunny side, in front of the wing. Astonishing show of clouds over the Atlantic: broken clouds, smooth clouds; regular clouds, chaotic clouds; layered clouds blaze with fire within as their ice crystals reflect the sun; filmy clouds draw a veil over the bronze-bright sunlit sea; fluffy clouds cast ominous shadows on the rippled surface; shafts of light penetrate mysterious cloud-castles and throw circles of brilliance. Meanwhile, the screen shows elephants being bathed in South India, and the ambient channel provides a backing of Amazonian birdsong. The letters CANA reflect in the polished engine cowling, above portholes, one of them mine. All conspiring to tell me, if I needed to be told, what a beautiful planet this is.
Here and nowI saw the rain-swept vista of the park,
under a sky so uniform and grey,
where leafless trees flung anguished branches high
in vain attempt to rip, to scratch, to mark;
it made me think, not for the first time, what
if I could pull aside the veil, or tear
the screen, to see reality appear,
blaze out behind illusion, would that not
be something? And reality may be
above the clouds, where sun-struck angels fly,
or further, world beyond world, where might ply
through perilous geometry of space
the gods--- but no, for here, before my face
this one leaf, leaf itself, is all! Just see!
At one moment I was amazed to see a vapour trail, holding level with us for a while. I looked away to watch a subsun, and it was gone. Then we flew into thin cloud: the earth was greyed out, the sun half-haloed. For most of the rest of the journey we were in cloud; but then it cleared to show us a fine display of textured cloud cover, like great frozen waves, topped by huge obelisks, touched by the westering sun; and later, a brilliant white field under a brilliant blue sky, which dissolved to reveal a copper-coloured under-layer. Later still, a sun-dog over the rivers and farmlands of Quebec, with mountains breaking through the plain like a school of strange whales.
Norman Biggs was on the plane, and we met up again at the baggage collection. We took the airport bus into town and the metro to the hotel (the same one that I stayed at in September, though in fact Norman has the room I was in then, and I am in a room with a bath and lots of hanging space). After time to shower and change, we went out to eat. Most places were closed, but the Italian restaurant where I ate with Martin Dunwoody last time was open and we went there. It was cheap and good. I think Norman was quite impressed with my local knowledge. I got back about eight and tried to read, but my eyelids wouldn't stay propped up.
We don't want to fight them but, by Jingo, we willAlso, when Samuel Johnson said "Patriotism is the last resort of the scoundrel", by patriotism he meant becoming a soldier, according to this book, "The Rise and Fall of the British Empire", by Lawrence James. This makes the statement much more explicable (if less subtle).
Went early to breakfast, where Norman, Tony and Laci soon arrived. I managed to persuade the first two to walk with me. It was cool but not unpleasantly so, but all the leaves had fallen from the trees. Lovely low sun across the river, the bright water bisected by the Champlain bridge.
This will be a somewhat technical meeting: we had the Wisconsin contingent today, and there will also be determinations of or finiteness theorems for the distance-regular graphs of not too large degree. I feel more out of place here than I did at Cayley graphs. But Laci was good, as usual.
I had lunch with Dom de Caen at the Indian restaurant. Then a large group were going to an Indian restaurant tonight, so I declined and came instead to the Commensal. I had with my supper a beer called "La fin du monde" (because it is 9% ABV).
Gert has asked me to chair the Problem Session on Thursday.
Last thing today I typed my poem onto Euclid, using vi over telnet (not to be recommended for those with weak nerves).
Université Laval has a big advertising poster according to which the main attraction is "Professeurs accessibles".
Anglo-French culture: My wash-basin has, on the right, an old tap labelled C, and on the left, a much newer tap labelled C.
Another question. Eiichi Bannai said yesterday that the lattice of imprimitivity systems in a commutative association scheme is modular. This is true; I just checked. But which modular lattices can occur? If we don't assume commutativity, then the lattice may not be modular: which lattices occur?
A beautiful sight outside the hotel: a line of raindrops on a branch, lit from behind by a street light.
The snow on top of the mountain was much deeper, about 2 inches in places, and there was quite a bit of ice on the steps. "There's a cold wind" said Tony as he did up one more button of his cardigan.
After our early finish I went down town, where I wandered round some of the underground shopping malls. I had one nasty moment when I went down an escalator into a department store and then couldn't find my way out! But I did manage to find "Longitude", by Dava Sobel, in paperback. I took it back to my hotel room and finished it before dinner, which I had at Ben's Deli, where I had Ben's famous smoked meat and Ben's famous fruit drink.
I had lunch with Sasha, and then chaired the problem session, at which not too many problems were presented, in part because several people (Sasha the worst culprit) took the chance to give long presentations. But at least I think I persuaded Greg Cherlin to include his triangle-free graph problem. A special (negative) case: show that, for some m, there is no triangle-free strongly regular graph in which any m nonadjacent points have a common neighbour.
Dinner at the Thai restaurant, and they had made it spicier this time. Drank lots of Fin du Monde.
On the sunward side, the sky was bright blue and the clouds golden. On the other side, the clouds were pink and full of snow, but a thin line of sky along the horizon was an astonishing pale green.
My talk went well. Lunch in Aux deux Gauloises was abominably slow, so I didn't get to phone Conway or read email, and was still 15 minutes late for Chris Godsil's talk. Ah well.
After the end of the workshop, and Laci's colloquium talk, there was a little reception. I talked to Greg (I have done his SRG problem with constant 5, and am confident I can reduce it to 4), Sasha, Eiichi, Chris, and Bill Martin. Laci gave me an office key; we will work tomorrow at 2pm.
I walked, a little later, over the hill. Much less pleasant than yesterday.
Brown leaves on white snow;I had mixed up the keys, but I went to Gert's office and sorted out which was which, then went down to Olga's. As I had guessed, the office key also opened the door to the corridor. So I worked there all morning. It was somewhat spooky, in a deserted building, behind a locked door, snow falling from a leaden sky outside, while I worked on a computer in London. I mailed Greg, sent Sasha a copy of the paper, looked for the manuscripts with Laci (found one but not the other).
echoes of "Fields of Gold", caught
on the radio.
I lunched at the Commensal. I got so cold going there that I had soup and hot food (which, unfortunately, was mostly some kind of textured protein).
After lunch, once I had finished reading things and was beginning to get bored, Laci came. We more-or-less agreed the version of the switching paper, but had rather more trouble with the other: we realised when we came to do the accounting at the end that the probabilistic lemma about the asymmetry of random hypergraphs was not what we needed. But there was no time to fix it, as we had to go to Gena's.
I tore back to the hotel and changed, and was only 20 minutes late. Laci and Olga didn't come for nearly an hour. Fortunately(?), Gena had had some disasters - burning oil and such like - so the meal was rather late. But no less delicious for that! Then we sang some songs, and indeed Gena and I kept on until nearly 5am. I walked home through icy but far-from-deserted streets.
I wandered out at about noon, saw Laci into his taxi, and then walked down to the Place des Artes. I found a little cafe for lunch, and then walked back along Ste Catherine, being seduced by various bookshops and record shops on the way. One shop had no less than four Joni Mitchell CDs for $8.99 each. I couldn't hold out completely, so I bought "Hejira".
It is really very cold, and the footpaths are treacherous I would certainly not like to be a beggar here (of whom there are quite a few). Mid-afternoon I went to Gena's. David and his two children were there; the kids drew and played noughts and crosses while we played some blues (things like Hoochie Coochie Man, Leopard-Skin Pillbox Hat, You Can't Always Get What You Want, and of course Desolation Row). Then David went off, and Gena and I had a quiet sit and talk and a bit to eat before going out to the concert.
This was a benefit concert for Nelson Symonds, an eminence gris of Montréal jazz guitar, who apparently just had a heart bypass operation (though he was at the concert and looked in quite good form). First we had a bass duet. One guy played acoustic bass, and he really was good. The other played a fretless six-string electric bass, which he could play a bit like a jazz guitar (three-note chords on the top strings) as well as a bass. Most effective, though Gena found the electric sound a bit too new-age.
Then a piano solo, and then a big band, led by the most authoritarian bandleader (calling out a soloist, or cueing a climax, with a single though extravagant gesture). They had taken so long setting up that the next act, a choir, had gone off in a huff. So instead we had a female jazz singer with guitar accompaniment. Someone read a poem while the next band set up, but I was tired and left.
The flight was not full, and was very good-natured. At one point, the pilot said, "After we push back from the stand, we will proceed to the de-icing pad, which is situated" (pause) "over there" (laughter from the cabin crew). De-icing involved having the wings sprayed with orange liquid from two big trucks. On each truck, one person had the job of directing operations from an elevated linesman-type crows-nest. What fun! Surprisingly, we were hardy delayed at all.
On the way I browsed the in-flight shopping catalogue. The most notable thing I saw was a turbo tie-holder.
We landed a bit early, but I just missed the Princeton bus and had to wait nearly an hour for another.
Seen on the way: a flag flying outside an old power station; a "driver safety educated" van with a toll-free number you can call "to comment" (the driver's ID is given), and on the same theme, a coach "driven with care" and "driven with pride"; a long line of pigeons on a wire, all facing the same way except for a couple of nonconformists; a faint sun dog in a drifting cloud. We turned off the turnpike and along a country road lined with harvested fields and leafless woods (some for sale for residential development), with the occasional isolated house, lawyer's office, or insurance company.
Then it became a bit more built-up, and we were in Princeton. The driver made a special stop for me, just a short walk from Fine Hall, and pointed me down the right road. I walked there (I had to ask once -- they don't put signs outside buildings here), went up in the lift, and find my way to John's office. He wasn't in, but his voice coming from down the corridor told me where he was, expounding at a blackboard in the corridor.
He took me to lunch at the bagel shop, and told me some amazing facts about Fibonacci numbers he had just discovered, and some other amazing things too. One of these was that a student of Richard Stanley has explained one number appearing, apparently, in the writings of Plutarch concerning compound statements built from ten propositions. Seemingly it is the number of ways to combine ten variables, not just with binary operators (that is the Catalan number), but with operators of arbitrary arity. He also told me about M13. If you take the projective plane of order 3, and place counters numbered 1 to 12 on the points (leaving one empty), and then make moves consisting of applying an element of the Klein group to any line containing an empty cell, the number of configurations is 13 times the order of M12; and if the hole is brought back to its initial position, the permutations of the numbers 1 - 12 obtained form M12. Moreover, both the outer automorphism and the Schur multiplier can be seen, the former by also putting numbers on the lines and requiring that the empty point and line are incident (returning both holes to their initial positions, the permutation of the lines is the dual of the permutation of the points), the latter by making the counters on the points two-sided, and turning over the two that are swapped in any move.
John also described to me his method for factorising in his head any number less than 5000. This relies on knowing the non-obvious composites below 1000 (there are 100 composites not divisible by 2, 3 or 5), and the fact that a bunch of consecutive numbers just above 2000 have all possible prime factors up to 71.
I then spent the afternoon (while John was busy) sitting in the common room. I wrote down the Fibonacci while my memory was fresh, and chatted to Martin Bridson for a while.
Then John came, we went to his apartment, had dinner at the Japanese restaurant, and went to the coffee house, talking the while about M13. He has promised to spend tomorrow writing it up: the overall shape has more or less become clear. We can get most of the properties of M12 from the construction. Apparently, there are similar things, with 3-sided counters, for the plane of order 2 (giving 3.A6.2), and the Petersen graph, with two adjacent holes (giving PGL(2,7)).
Then we went and worked on a list from Neil Sloane. He and John are re-doing the 4-dimensional Archimedean polytopes. Neil had computed 600 odd shapes of corners, and we analysed these to see whether they could correspond to vertex figures or not. (Not all of them!) I started to read my email, but John McKay came on wanting to talk. So I talked to him a bit, and then John did. One of the topics was another interesting problem, the cost of a group. You are given letters representing distinct generators, and may ask for the product of two letters (which may be a new letter). Each query costs 1 cent, and you have to identify the group. There is a group of order 127.(2127-1) costing only 10 cents.
There is a group in this game: each move is a permutation on the bijective functions from the point set P to 0..12; if it is a move on the line L, it fixes all those functions which don't map a point of L to 0. So we have a permutation group on 13! things generated by 39 involutions. I convinced myself that it is M12 wr A13 (for it commutes with the group S12 of permutations of 1..12, and so lies in S12 wr S13). I'd hoped to get something more interesting. Oh well.
In the afternoon John sat and typed, and finished the first draft by 6:30. It was quite painful to watch him using vi: he wanted the thing laid out with lines of roughly the right length, without understanding the TeX convention, without knowing about J or any movement commands except the arrow keys.
We went to the Japanese restaurant again; we shared a bridge of sushi and sashimi, my treat. Then we went to the coffee shop, where we did more of the Archimedean polytope vertex-figure clumps, decided what revisions needed to be done on the paper, and so to bed. Before leaving the coffee shop, I extracted a promise that he would email the revision before the end of the week; but, just in case, I have all the data, including the figures.
I caught the 9 o'clock dinky. At Princeton Junction, they announced that all trains were 15 to 30 minutes late, just as a train pulled in.
We pottered past little towns, and I pondered the problem of drawing Conway's PG(2,3) in LaTeX. I had just narrowly failed, when we came into Newark Penn Station. In the clear air, New York City shimmered in the distance, scarcely more substantial than the clouds behind it.
There was a scrum at the airport - Thanksgiving again - but I got checked in after quite a wait. I was a bit surprised that we were taken to the plane in one small shuttle bus, but it turned out to be a little propeller plane, about 50 seats, and not at all full. I got good view of New York on takeoff, and the wide St Lawrence on landing. Most of the trip I wrestled unsuccessfully with the diagram. I think I may abandon the idea of having the Y axis vertical: if I make the figure symmetrical there are only half as many slopes to fit.
And so home - but that is all I got around to writing!