Looking back: 2001

The 1968 film 2001: A Space Odyssey suggested that we would have extensive space flight in 2001. That turned out not to be the case. What we did get was the September 11 attacks on the USA and the military conflicts which followed. Nevertheless, NASA commemorated the film with the 2001 Mars Odyssey orbiter.

Films of 2000 included the superb The Lord of the Rings: The Fellowship of the Ring, several good animated films (including Monsters, Inc., Shrek, and Hayao Miyazaki’s Spirited Away), the wonderful French film Amélie, some war movies (Enemy at the Gates was good, but Black Hawk Down distorted the book too much for my taste), the first Harry Potter movie, and an award-winning biographical film about the mathematician John Nash.

In books, Connie Willis published Passage, one of my favourite science fiction novels, while Ian Stewart explained some sophisticated mathematics simply in Flatterland.

Saul Kripke (belatedly) received the Rolf Schock Prize in Logic and Philosophy for his work on Kripke semantics, while Ole-Johan Dahl and Kristen Nygaard (also belatedly) received the Turing Award for their work on object-oriented programming languages (both these pioneers of computing died the following year).

The year 2001 also saw the completion of the Cathedral of Saint Gregory the Illuminator in Armenia, which I have sadly never visited.

In this series: 1978, 1980, 1982, 1984, 1987, 1989, 1991, 1994, 2000, 2001, 2004, 2006, 2009.


Houston, we have a problem

Some years ago, I posted the chart above, inspired by a classic XKCD cartoon. The infographic above shows the year of publication and of setting for several novels, plays, and films.

They fall into four groups. The top (white) section is literature set in our future. The upper grey section contains obsolete predictions – literature (like the book 1984) set in the future when it was written, but now set in our past. The centre grey section contains what XKCD calls “former period pieces” – literature (like Shakespeare’s Richard III) set in the past, but written closer to the setting than to our day. He points out that modern audiences may not realise “which parts were supposed to sound old.” The lower grey section contains literature (like Ivanhoe) set in the more distant past.

The movie Apollo 13 has now joined the “former period piece” category. Released in 1995, it described an event of 1970, 25 years in the past. But the ill-fated Apollo 13 mission of 11–17 April 1970 is now 51 years in the past; the movie is closer to the event than it is to us (although the phrase “Houston, we have a problem” – in real life, “Houston, we’ve had a problem” – has become part of the English language).

The image shows the real-life Apollo 13 Service Module, crippled by an explosion (left), together with a poster for the 1995 movie (right). Maybe it’s time to watch it again?


Cistercian numerals

Somebody recently pointed me at Cistercian numerals (above), an interesting base-10 numeral system used by Cistercian monks in the Low Countries and northern France from the 1200s to the 1500s (that is, after the Liber Abaci introduced Hindu-Arabic numerals to Europe, but apparently based on an older English system, not on that).

Most extant uses of the system relate to dates and item numbering, rather than arithmetic. This online conversion tool will let you experiment with the system. It is interesting to note the relationships 5 = 4 + 1, 7 = 6 + 1, 8 = 6 + 2, and 9 = 8 + 1 = 7 + 2 = 6 + 2 + 1.


The Santa Fe Trail #4


NPS map of the Santa Fe Trail in 1871 (click to zoom; more maps here)

The American Solar Challenge is on again in 2021, and includes a road race along the Santa Fe Trail on 4–7 August, from Independence, MO to Santa Fe, NM (exact route still to be decided).

To get myself in the mood, I’ve been reading Land of Enchantment, the memoirs of Marion Sloan Russell, who travelled the Santa Fe Trail multiple times. After marrying, she was an “army wife” for some time, before setting up a trading post beside the Trail. In 1871, she moved to a ranch in the mountains west of Trinidad, CO, where her husband was murdered during the Colfax County War. Towards the end of her life she visited many important sites along the Trail. They were already falling into ruin:

At Fort Union I found crumbling walls and tottering chimneys. Here and there a tottering adobe wall where once a mighty howitzer had stood. Great rooms stood roofless, their whitewashed walls open to the sky. Wild gourd vines grew inside the officers’ quarters. Rabbits scurried before my questing feet. The little guard house alone stood intact, mute witness of the punishment inflicted there. The Stars and Stripes was gone. Among a heap of rubble I found the ruins of the little chapel where I had stood—a demure, little bride in a velvet cape—and heard a preacher say, ‘That which God hath joined together let no man put asunder.’

Marion Sloan Russell died in 1936 (aged 92) after being struck by a car in Trinidad, CO. She is buried in Stonewall Cemetery.


Fort Union in 2006 (credit: Scott; click to zoom)

Other posts in this series: Santa Fe Trail #1, Santa Fe Trail #2, Santa Fe Trail #3, Santa Fe Trail #4.


The Santa Fe Trail #3


NPS map of the Santa Fe Trail in late 1866 (click to zoom; more maps here)

The American Solar Challenge is on again in 2021, and includes a road race along the Santa Fe Trail on 4–7 August, from Independence, MO to Santa Fe, NM (exact route still to be decided).

To get myself in the mood, I’ve been reading Land of Enchantment, the memoirs of Marion Sloan Russell, who travelled the Santa Fe Trail multiple times. After marrying, she was an “army wife” for some time, before setting up a trading post beside the (somewhat shorter in 1866) Santa Fe Trail at Tecolote, NM (about 15 km south of Las Vegas, NM):

We had five living rooms behind the store. They were cool and pleasant. The thick stone walls resisted both heat and cold. The windows were long and narrow running from ceiling to floor. I draped them with a gay silken print. The floor I had covered with Navajo rugs … Often I have heard old-timers laughing about the heat and the dust of the desert. I have heard them say jokingly that Hell would seem cool after living in Santa Fé. I had heard them say that the burning sands of the desert had sucked old-timers so dry that they could not pray. I had laughed with them …

Hopefully solar cars in the American Solar Challenge do not find the temperatures quite so hellish. The chart below shows average maximum July temperatures (early August temperatures are on average only about 0.5°C cooler, and may indeed be warmer, which means that temperatures inside the vehicles will be very hot):


Click to zoom; map produced using climate data from worldclim.org

Other posts in this series: Santa Fe Trail #1, Santa Fe Trail #2, Santa Fe Trail #3, Santa Fe Trail #4.


The Santa Fe Trail #2


NPS map of the Santa Fe Trail “Mountain Route” (click to zoom; more maps here)

The American Solar Challenge is on again in 2021, and includes a road race along the Santa Fe Trail on 4–7 August, from Independence, MO to Santa Fe, NM (exact route still to be decided).

To get myself in the mood, I’ve been reading Land of Enchantment, the memoirs of Marion Sloan Russell, who travelled the Santa Fe Trail multiple times. Her third trip was in 1860, at the age of 15, travelling from Fort Leavenworth along the “Mountain Route” or “Upper Crossing.” This route avoided Indian raids along the Cimarron Cut-Off. The Mountain Route crosses the 7,840 ft (2,390 m) Raton Pass:

Breaking camp while it was still early, our cavalcade began the steep and tortuous ascent of the Raton Pass. Today we glide easily over hairpin curves that in 1860 meant broken axles and crippled horses. The trail was a faint wheel mark winding in and out over fallen trees and huge boulders.

If the American Solar Challenge follows the Mountain Route, solar cars will hopefully have an easier time on the modern road. The “big climb” at the 2018 American Solar Challenge (following the Oregon Trail) was 902 m in 35 km (2.6%). Starting from Trinidad, CO, the Raton Pass has a similar climb of 558 m in 22 km (2.5%), with a maximum grade of 6% on the steepest sections.


Raton Pass in October 2009 (credit: Chris Light; click to zoom)

Other posts in this series: Santa Fe Trail #1, Santa Fe Trail #2, Santa Fe Trail #3, Santa Fe Trail #4.


The Santa Fe Trail #1


Map of the Santa Fe Trail (credit: NPS; click to zoom)

The American Solar Challenge is on again in 2021, and includes a road race along the Santa Fe Trail on 4–7 August, from Independence, MO to Santa Fe, NM (exact route still to be decided).

To get myself in the mood, I’m reading a second-hand copy of Land of Enchantment, the memoirs of Marion Sloan Russell, who first travelled the Santa Fe Trail in 1852 as a young girl of seven (following the southern route, the “Cimarron Cut-Off”) under the leadership of François Xavier Aubry:

Each night there were two great circles of wagons. Captain Aubry’s train encamped a half mile beyond the government’s. Inside those great circles the mules were turned after grazing, or ropes were stretched between the wagons and thus a circular corral made. Inside the corral were the cooking fires, one for each wagon. After the evening meal we would gather around the little fires. The men would tell stories of the strange new land before us, tales of gold and of Indians. The women would sit with their long skirts drawn up over a sleeping child on their laps. Overhead brooded the night sky, the little camp fires flickered, and behind us loomed the dark hulks of the covered wagons. … It was strange about the prairies at dawn, they were all sepia and silver; at noon they were like molten metal, and in the evening they flared into unbelievable beauty—long streamers of red and gold were flung out across them. The sky had an unearthly radiance. Sunset on the prairie! It was haunting, unearthly and lovely.

Not everything was quite so lovely; a theft in Santa Fe forced Marion’s widowed mother to abandon a further trip to California. Instead, she ran a boarding house: first in nearby Albuquerque, and later in Santa Fe itself. Let’s hope things go more smoothly for the solar cars of 2021.

Other posts in this series: Santa Fe Trail #1, Santa Fe Trail #2, Santa Fe Trail #3, Santa Fe Trail #4.


Triboelectricity

The triboelectric effect was discovered 2600 years ago by Thales of Miletus. When items in this illustrated (incomplete) list are rubbed together, the low-numbered item gains a positive charge, and the high-numbered item gains a negative charge.

For example, glass rubbed with silk (or, even better, polyester) gains a positive charge, once called “vitreous electricity.” Amber rubbed with wool gains a negative charge, once called “resinous electricity.” Indeed, our word “electron” comes from the Greek ἤλεκτρον, meaning “amber.”


Infinitesimal by Amir Alexander: a book review


Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander (2014)

I recently read Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander. This book concentrates on the “indivisibles” of Bonaventura Cavalieri and the “infinitesimals” of John Wallis (the man who introduced the ∞ symbol). As a history of pre-calculus, that’s rather incomplete. There are also some errors, noted by Judith Grabiner in her review for the MAA.

Alexander portrays the Jesuits as the “bad guys,” suppressing the idea of “indivisibles,” even though interesting and useful mathematical results can be obtained by using them. However, Alexander does not fully explain the Jesuits’ actions. There is not a word about their struggle with the Dominicans for intellectual leadership of the Catholic Church (although this played a major part in the Galileo saga). Nor does he explain the link between defending Aristotle and defending the doctrine of Transubstantiation. And, of course, the critics of Cavalieri and Wallis were actually quite correct. “Infinitely small numbers” greater than zero do not exist, and calculus did not have a rigorous foundation until the work of Cauchy and Weierstrass in the 1800s.

I was left rather disappointed with this book. GoodReads rates it 3.83, but I’m only giving it two stars.


Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander: 2 stars