Please excuse me for borrowing a couple of terms from elementary mathematics:
— A relation is said to be
reflexive if it works in both directions. For example, "
can see" is reflexive in the sense that, if John can see Mary, then normally Mary can see John. But "
loves" is not necessarily reflexive, because John can love Mary whereas the sentiment might not be reciprocal.
— A relation is said to be
transitive when its effects are, as it were, cumulative. For example, "
is greater than" is transitive. If X is greater than Y, and Y is greater than Z, then X is necessarily greater than Z.
A few days ago, while watching my daughter and my dog scampering over the slopes at Gamone, I found myself wondering, for a few instants, whether "
can see" might be, not only a reflexive relation, but transitive too. For example, if I can see simultaneously both my daughter and my dog up on the hillside, does this mean that they can see one another? This, of course, is a stupid question. Clearly, the answer is no. For example, you might be able to see two individuals in adjacent rooms, whereas their mutual vision is blocked by a wall. In other words, "
can see" is not a transitive relation.
Here's a view of the circus of Choranche, as seen from my house:
Of an evening, I often see a bright electric lamp at the far end of the valley, at the spot where I've put a red dot. This lamp has always intrigued me, for three reasons. First, it's the unique source of light in this entire direction. (In other words, as soon as the Sun goes down, when the lamp is unlit, the entire scene of the photo is plunged in darkness.) Second, I've never been able to determine with certainty the precise place where this light is located. Third, the lamp is only lit at certain short periods of the year, which don't necessarily seem to coincide with holiday dates.
Behind the red dot in the photo, the massive rock wall that fills in the horizon between the cliffs of Presles and the slopes of the Bournillon is called Chalimont. On the far side of their crest, the vast forest of Herbouilly stretches out over the Vercors plateau in the direction of Villard-de-Lans.
Just beneath the red dot in the photo, you can see a curved line of clifftops, lying above the River Bourne, which tumbles down from a break in the Chalimont (hidden, in the photo, by the cliffs of Presles). In the middle of this curved line, some seven kilometers from my house (as the crow flies), the lowest point is a pass (for experienced rock-climbers) known as the
Devil's Doorway. A nearby hole in the cliff is referred to as the
Gaul's Cave. Besides, it's perfectly possible that human Bronze-Age cavemen might have used this place, two or three thousand years ago, as a base camp for their summer hunting season. And somewhere between the red dot and the curved line of clifftops, there's a sizable village, St-Julien-en-Vercors, lying alongside a major road that runs from the Bourne across to the village of La-Chapelle-en-Vercors (located behind the Bournillon plateau).
At the end of my article of 26 December 2009 entitled
More fallen rocks [display], I explained that, to escape from Choranche, I have to choose a route up over the surrounding mountains. The other day, I left early and headed up towards St-Julien-en-Vercors, while saying to myself that I might find time to finally elucidate the puzzle (which arose for the first time in May 2004) of the lamp at the end of the valley. By chance, the first villager I encountered happened to be (I learned later) the most informed person in existence concerning St-Julien and its surroundings. As soon as I told him I came from Choranche, he said
"I've never liked that village. No charm whatsoever." I found this frankness reassuring. There was no chance that this fellow would tell me bullshit. In fact, within a few minutes, we had become firm friends, and he told me everything I needed to know about the mysterious lamp. So, here's a summary of the affair.
The light comes from a forestry hut, high up on the slopes of the Chalimont, several hundreds meters above the village of St-Julien. The hut and a surrounding forest zone belong to a retired member of the French merchant navy, who lives down at Cassis, near Marseille. He and his wife drive up to the Vercors and stay up in the hut (accessible only on foot, and surrounded by snow at present) whenever the owner has to handle various aspects of the management of his trees. Since I left my name and address, the fellow phoned me up yesterday, introducing himself with humor as my "next-door neighbor". This afternoon, I used a telephoto lens to take a photo of what I believe to be his log cabin:
[Click the photo to see an enlarged version.]It sure looks icy up there. It seems to be so far away, and yet this Siberian scene lies just at the end of my long-focal lens.
Now, let me return to the definitions of mathematical relations at the start of this article. I said that the "
can see" relation is reflexive. So, since I can see the lamp of this log cabin up on the slopes of the Chalimont, then the occupants should be able to see the lights of my house at Gamone. When I asked the owner what he could actually see from his log cabin when he looked in the direction of Choranche, I was surprised to learn that he can apparently see many interesting places. If I understand correctly, of an evening, he can see so many lights that he's not at all sure which one is my house at Gamone. Usually, he has a clear view of the
autoroute that leads south in the direction of the Mediterranean. Furthermore, on clear days, he can often detect a celebrated mountain range in the south of France: the
Cévennes.
That last detail set me thinking. If I can see my neighbor up on the slopes of the Chalimont, and he can see straight down to the south of France, then what a pity that the "
can see" relationship is not transitive... otherwise I too should be able to gaze down at the south of France. This, of course, is totally unthinkable. From Gamone, I can't even see as far south as the first village in the Drôme, Saint-Eulalie, which is no more than a kilometer away.
During the first half of the 19th century, the French engineer
Claude Chappe invented and installed a vast semaphore system throughout France, which concretized the transitive nature of the "
communicate with" relation. During the Napoleonic Wars, for example, a series of Chappe towers could receive and retransmit information so rapidly that a message could be sent from one side of France to the other in a quarter of an hour. Now, that approach would in fact enable my Chalimont neighbor to inform me visually, every evening, what the weather had been like down in the south of France during the afternoon. He could use his powerful lamp to send me messages in Morse code. In fact, this won't be necessary, because I've already given him, not only my phone number, but my email address. Still, I get a thrill out of thinking that, at Gamone, I'm a mere hair's breadth away from being able to gaze down upon Provence.
In this delightful banner, an animated apple (the one on the left) actually dropped from the tree, just a few seconds after its display. Consequently, I had to make several attempts to be quick enough to obtain an acceptable screen capture of the banner... before the falling apple hit the "ground" below Google's argument box.
I, too, behaved as a good citizen in baring courageously my arm a few weeks ago. But there are still a hell of a lot of unused shots in France, and nasty critics are starting to suggest that Roselyne may have overestimated the requirements. What we need now is some creative thinking about ways and means of getting rid of all the surplus stuff in such a way that France doesn't lose too much money because of this fiasco. In the environmental domain, it would be an interesting idea to see if flu vaccine can be used as an additive to enhance the efficiency of new kinds of ecological fuel products for automobiles. We should investigate the possibility that flu vaccine might give rise to spectacular increases in productivity in agricultural domains such as wheat, soja and fruit and vegetables of all kinds. Then, we must not forget that the cycling season will be starting soon. That should be an excellent commercial outlet for a lot of this stuff... maybe mixed with other molecules to create an explosive cocktail. Last but not least, it's perfectly plausible that, with a bit of good marketing, male users of the Internet could be persuaded that a series of flu shots, spread out over a month or so, can result in an extra few centimeters at the level of their vital organ.
Half a century ago, on 4 January 1960, much of France was covered in snow... like today. A celebrated French writer, Albert Camus, was returning to Paris in a Facel Véga sports car driven by his editor, Michel Gallimard. On the rear seat of Gallimard's powerful automobile, his wife Janine and her daughter Anne were accompanied by their Skye terrier. They had left Lourmarin in Provence on the previous morning and stayed overnight in a small inn called the Chapon Fin at Thoissey, in the valley of the Saône, to the north of Villefranche. After Sens, the road was generally straight, and bordered by plane trees... like today, except that the road was narrower at that time, and there were trees on both sides.
Heading westward towards Fontainebleau on a damp road at about 150 km/hour, Michel Gallimard suddenly lost control of his automobile at a place called Petit-Villeblevin. It zigzagged, left the road and wrapped itself around a plane tree. Camus died instantly, and Michel Gallimard succumbed to his wounds six days later. The two women survived miraculously, but their dog Floc had disappeared.
The following three images of the wreckage have been extracted from a silent news film [display]:
At that time, I was a 19-year-old computer programmer with IBM in Sydney. I had read English translations of three or four books by Camus, including The Myth of Sisyphus (which I still have with me at Gamone), and I was totally under the charm of this writer... whom I imagined, fuzzily, as an existentialiste, like Jean-Paul Sartre. It's not an exaggeration to say that one of the principal motivations for my initial pilgrimage to France in 1962 was the lure of the spirit of Albert Camus.
If Nicolas Sarkozy has his way, the remains of the writer will soon be transferred to the Panthéon in Paris... which is surely one of the silliest ideas that the president has ever imagined.
After burrowing into the snow with her snout, and rolling on her back, she shot off like a husky.
Admire the aerodynamic form of her ears, like the stabilizing fins of a Formula-1 racing car. Once she got up speed, she started to circle the yard like a greyhound in a racing stadium.
I have the impression that much of the pleasure, for Sophia, comes from the soft texture of the snow beneath her paws. At the seaside, too, she's thrilled by the possibility of racing across sandy beaches. The snow universe has the magical characteristic of wrapping itself softly around her paws, her snout and her body.
[Click the graphic to get a more readable view]
Yesterday, I was thrilled to receive a friendly comment from a woman in Australia named Kylie Clarke, whose great-great-uncles Thomas Clarke [1840-1867] and John Clarke [1844-1867] were prominent bushrangers in the Braidwood district, executed by hanging in Sydney on 25 June 1867. For a while, my great-great-uncle William Hickey [1818-1901] was a member of their gang.
Of an evening, I often see a bright electric lamp at the far end of the valley, at the spot where I've put a red dot. This lamp has always intrigued me, for three reasons. First, it's the unique source of light in this entire direction. (In other words, as soon as the Sun goes down, when the lamp is unlit, the entire scene of the photo is plunged in darkness.) Second, I've never been able to determine with certainty the precise place where this light is located. Third, the lamp is only lit at certain short periods of the year, which don't necessarily seem to coincide with holiday dates.
[Click the photo to see an enlarged version.]
During the first half of the 19th century, the French engineer Claude Chappe invented and installed a vast semaphore system throughout France, which concretized the transitive nature of the "communicate with" relation. During the Napoleonic Wars, for example, a series of Chappe towers could receive and retransmit information so rapidly that a message could be sent from one side of France to the other in a quarter of an hour. Now, that approach would in fact enable my Chalimont neighbor to inform me visually, every evening, what the weather had been like down in the south of France during the afternoon. He could use his powerful lamp to send me messages in Morse code. In fact, this won't be necessary, because I've already given him, not only my phone number, but my email address. Still, I get a thrill out of thinking that, at Gamone, I'm a mere hair's breadth away from being able to gaze down upon Provence.
He was smart enough to send off his shit email to a list of "undisclosed recipients". Nevertheless, Fadhil doesn't seem to have a firm grip on the English language. Somebody had apparently informed him that emails of this kind fall into a category known as spam. So, to make sure that his email is recognized as belonging to the correct category, Fadhil has inserted the word SPAM, explicitly, at the head of his subject line. That way, there's no way in the world that his email might be mistaken for something that it's not intended to be.
My article of 26 November 2009 entitled Damnable Irish Catholic behavior [display] evoked a report on disgusting sexual crimes involving children committed by Catholic personnel in Ireland. Today, it's frankly preposterous that this same nation should be intent upon promulgating a law against blasphemy. This ugly law must be repealed as soon as possible!
Five minutes ago, when I took this photo in the kitchen, not even the flash disturbed the deep slumber of my darling dog. At the present moment, on the contrary, after suddenly waking up and demanding that I open the door, she's racing around and barking on the slopes. I've often said that it takes no more than a farting fox on the crest of a nearby mountain to cause Sophia to spring back into action.
I've just noticed a press article indicating that, throughout France this evening, some 45,000 police and gendarmes are deployed to make sure that peace prevails.
An article in The New York Times reveals the existence of a ray of hope [display]. It has always saddened my heart to hear that these fabulous beats have been suffering and dying, and it would be utterly marvelous if modern genetics could save them.
Within the system, this modification appears to be transparent. So, I don't have to notify anybody in any way whatsoever.
Whenever I stroll through London's Trafalgar Square, I recall this photo of the 87-year-old white-maned philosopher standing among the lions at the foot of Nelson's Column at a 1959 rally of the Campaign for Nuclear Disarmament.
Since 1978, an association of freethinkers named the Freedom From Religion Foundation, based in Wisconsin, has been striving to erode the grip of God's trustees. Among other things, they've got around to designing what look like stained-glass windows of a new kind. Here's their Dawkins model:
[Click the banner to display a humongous version]
[Click the portraits to display the letter]
An English translation of Lévy's initial reaction to the Polanski case was published on 27 October 2009 in the US liberal news website co-founded by the Greek-American author and syndicated columnist Arianna Huffington. [Click the banner to read this article]
However, I'm thinking of using Twitter systematically to announce new blog posts. For the moment, I haven't made up my mind whether to make such announcements in English, in French or in both languages.
First, of course, this erudite Oxford professor has a profound mastery, not only of zoology (his basic field), but of neighboring sciences such as biology and paleontology. Besides, Dawkins is quite at ease in fields such as games theory and statistics, and he's even a competent computer programmer. The second obvious ingredient of Dawkins' success as a writer is his virtuosity in the domain of the English language, which he handles constantly with the sensitivity of a poet. His scientific and literary achievements are reflected in the fact that Dawkins, in Britain, is both a Fellow of the Royal Society and a Fellow of the Royal Society of Literature. When appropriate, he can fall deliberately into the casual vernacular of a journalist writing in a popular magazine, just as he can switch on instantly, if need be, the didactic language of a schoolmaster. He can throw a tender personal anecdote into the middle of pages of scientific explanations:
The first Dawkins book I read was The Blind Watchmaker, which stunned me instantly. That was the first time I had ever heard of the possibility (today, I would say the certainty) that, on the early inanimate planet Earth, a crude mineral self-copying entity composed solely of clay or crystal had evolved into the fabulous DNA replicator that has since become the unique basis of all life on the planet.
Several of these delightful creatures are lodged here at Gamone, where they offer me aeronautical shows in the twilight on late summer afternoons... like the fruit bats in my native Grafton.
In Climbing Mount Improbable, Dawkins expresses his utter amazement concerning another creature of which there are ample specimens here at Gamone: the spider. Their web-building operations, as explained by Dawkins, are fantastic.
Now, insofar as I'm particularly fond of figs (receiving fruit from Madeleine and Dédé, as well as from Bob's tree... while waiting for my own—given to me by Natacha and Alain—to become productive), I had imagined that I probably knew at least a thing or two about this fruit. Well, it turns out that, before reading Dawkins, I was totally and dismally ignorant on the subject of figs. First, what we imagine as the so-called "fruit" is not at all a true fruit. It's rather a strange garden of countless delicate fig flowers. What we see as the fig's skin might be thought of as the "earth" in which these flowers are growing. And the garden has curved, over evolutionary time, into a concave bulb that hides the flowers. Furthermore, inside this closed garden, the fig flowers live and procreate thanks to the complex services rendered by a community of devoted little male and female wasps, whose entire existence and survival are inextricably linked to the fig tree in question. In order to understand what happens in this mysterious garden, I started to draw a few diagrams like this one, which indicates the four principal actors: male and female fig flowers, female wasps and wingless male wasps.
The female wasps (made pregnant prior to their actual birth) stuff pollen from male flowers into their breasts and escape from the fig garden through holes in the "earth" burrowed by males. As soon as a female wasp locates another "garden" with female flowers waiting to be pollinated, she crawls in through the tiny hole at the extremity of the fig, maybe tearing off her wings in the process. Apparently we crunch such microscopic Agaondae wasps every time we bite into a fig, but they can do us no harm. Within the confines of this blog, I certainly don't intend to try to delve more deeply into the fabulous fig story. In any case, Dawkins has already told this story fully and splendidly. I recommend his book to everybody who's sensitive to all things bright and beautiful, all creatures great and small.
[Click the photo to visit their website.]
When you slit open the cellophane, the contents emit a wonderful aroma of damp moss and wood.
Once the moss is shaken off, the moist bare peoney roots have such a delightful wine-hued aspect and vegetal aroma that you might feel like eating them. (Well, that's what I felt.)
I'll wait until spring before describing exactly what I've now planted at Gamone in the way of roses and peonies.
