## From the Venetian Quarter

In 1204 the Fourth Crusade, reaching the peak of its mission to undermine Christianity in the eastern Mediterranean, sacked Constantinople and established a Latin ruler in the remains of the Roman Empire, which we dub today the Byzantine Empire. This I mention because I’m reading John Julius Norwich’s A History of Venice, and it discusses one of the consequences. Venice had supported the expedition, in no small part to divert the Fourth Crusaders from attacking its trading partners in Egypt, and also to reduce Constantinople as a threat to Venice’s power. Venice got direct material rewards too, and Norwich mentions one of them:

When, on 5 August 1205, Sebastiano Ziani’s son Pietro was unanimously elected Doge of Venice, the first question that confronted him was one of identity. To the long list of sonorous but mostly empty titles which had gradually become attached to the ducal throne, there had now been added a new one which meant exactly what it said: Lord of a Quarter and Half a Quarter of the Roman Empire.

This I mention because the reward of three-eighths of the Byzantine Empire (the Byzantines considered themselves the Roman Empire, quite reasonably, and called themselves that) is phrased here in a way that just wouldn’t be said today. Why go to the circumlocution of “a quarter and half a quarter” instead of “three-eights”?

## Arthur Christmas and the End of Time

In working out my little Arthur Christmas-inspired problem, I argued that if the reindeer take some nice rational number of hours to complete one orbit of the Earth, eventually they’ll meet back up with Arthur and Grand-Santa stranded on the ground. And if the reindeer take an irrational number of hours to make one orbit, they’ll never meet again, although if they wait long enough, they’ll get pretty close together, eventually.

So far this doesn’t sound like a really thrilling result: the two parties, moving on their own paths, either meet again, or they don’t. Doesn’t sound quite like I earned the four-figure income I got from mathematics work last year. But here’s where I get to be worth it: if the reindeer and Arthur don’t meet up again, but I can accept their being very near one another, then they will get as close as I like. I only figured how long it would take for the two to get about 23 centimeters apart, but if I wanted, I could wait for them to be two centimeters apart, or two millimeters, or two angstroms if I wanted. I’d pay for this nearer miss with a longer wait. And this gives me my opening to a really stunning bit of mathematics.

## Six Minutes Off

Let me return, reindeer-like, to my problem, pretty well divorced from the movie at this point, of the stranded Arthur Christmas and Grand-Santa, stuck to wherever they happen to be on the surface of the Earth, going around the Earth’s axis of rotation every 86,164 seconds, while their reindeer and sleigh carry on orbiting the planet’s center once every $\sqrt{2}$ hours. That’s just a touch more than every 5,091 seconds. This means, sadly, that the reindeer will never be right above Arthur again, or else the whole system of rational and irrational numbers is a shambles. Still, they might come close.

After all, one day after being stranded, Arthur and Grand-Santa will be right back to the position where they started, and the reindeer will be just finishing up their seventeenth loop around the Earth. To be more nearly exact, after 86,164 seconds the reindeer will have finished just about 16.924 laps around the planet. If Arthur and Grand-Santa just hold out for another six and a half minutes (very nearly), the reindeer will be back to their line of latitude, and they’ll just be … well, how far away from that spot depends on just where they are. Since this is my problem, I’m going to drop them just a touch north of 30 degrees north latitude, because that means they’ll be travelling a neat 400 meters per second due to the Earth’s rotation and I certainly need some nice numbers here. Any nice number. I’m putting up with a day of 86,164 seconds, for crying out loud.

## Wednesday, June 6, 1962 – Food Contract, Boilerplate Purchase

The Manned Spacecraft Center has awarded to the Whirlpool Corporation Research Laboratories of Saint Joseph, Michigan, a contract to provide the food and waste management systems for Project Gemini. Whirlpool is to provide the water dispenser, food storage, and waste storage devices. The food and the zero-gravity feeding devices, however, are to be provided by the United States Army Quartermaster Corps Food and Container Institute, of Chicago. The Life Systems Division of the Manned Spacecraft Center is responsible for directing the program.
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## Friday, June 1, 1962 – Operations Coordination Meeting, Astronaut Applications Close

Today’s was the first spacecraft operations coordination meeting. Presented at it was a list of all the aerospace ground equipment required for Gemini spacecraft handling and checkout before flight.

June 1 was also the nominal closing date for applications to be a new astronaut. Applications were opened April 18. The plan is to select between five and ten new astronauts to augment the Mercury 7.

## Thursday, May 24, 1962 – Parachute testing starts

At the Naval Parachute Facility in El Centro, California, North American completed a successful drop test of the emergency parachute recovery system, using a half-scale test vehicle.
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