Asymptotes

Sarah Elliott

x. The epigram to the chapter in the Arcades Project called Paris, Capital of the 19th Century is a poem by Nguyen-Trong-Hiep. It is called Paris, Capital of France:

The waters are blue and the vegetation pink;
evening is sweet to behold;
People are out walking. Great ladies promenade;
and behind them walk the small ladies.

1. For example I saw three young men in long garments walking down the street, they were very tall and dark skinned, the garments were made of thin white material, a thin muslin, an iridescent viscose, some kind of shiny synthetic material. Underneath they were additionally clothed, in typical western summer wear. Two wore sneakers, and one walked barefoot.

2. Parallel lines are two lines which never intersect.

3. It was not until I noticed this that I understood that, generally, the groups’ attire was distinctly foreign to the sartorial norm of Clinton Hill. The garments were loose and, although these young men were quite tall, fell all the way to the ground from their straight shoulders.

4. The Palace of Versaille was the functional capital of France for over a hundred years. Originally a hunting lodge built by Louis XIII, the palace was expanded to one of the largest in the world by Louis XIV, who eventually moved the court from Paris to Versaille in 1682.

5. I continued to look back over my shoulder at the retreating frames of these young men, until a building or some trees obscured them completely from view.

6. In particle physics for every particle there is a corresponding anti-particle, which has identical mass and spin.

7. I was quite struck that I had not noticed these oddly dressed men even though I had certainly seen them, maybe even looked at them for a moment until I noticed that one of them was barefoot. The garments themselves were so out of place- however they seemed to have the forms of other, more familiar, garments. They had rectangular yokes and were gathered at the shoulders similarly to graduation robes or the robes that Catholic Priests wear, and rounded collars with an opening coming down in a soft “v” in the front, similar to ones I’ve seen on some Indian men’s garments. But they were certainly not, from what I could tell, any of these. Perhaps, I continued to think, I was so certain of this because these young men, about 15 or 16, appeared neither as graduates, or as priests, or as Indian men. Neither did they appear to be masquerading- they walked with easy purpose, without self-consciousness.

8. During the revolution, the royal family was forced to leave Versaille, and Louis XVI, Marie-Antoinette, the dauphin and the dauphine moved into the Palais du Tuilaries in Paris. Over the subsequent hundred years, although there were attempts towards preservation, and parts of the palace were made into museum galleries, much of  Versaille was left to deteriorate; its art and ornamentation being sold off or put into various museum collections. It was later occupied by Napolean and his wife during the first empire, then Louis-Phillipe, the emperor of the July Monarchy. Louis-Philipe re-proposed the palace as a museum, which eventually opened in 1837. Since Louis-Philipe the palace has not been inhabited. During the 20th century the palace underwent massive renovation and restoration, becoming the tourist attraction that it is today, and was designated a world heritage site by UNESCO in 2007.

9. I was on my way to the train, which I would take to a place where I would make a performance. The performance would include showing and constructing various representations of styles of swimming pools that a particular company makes. It also included an aria from the opera ‘La Boheme’, by Puccini, in which one of the protagonists introduces herself, emphasizing several times that though she is often called by one name, her real name is something else.

10. The laws of nature are applicable to anti-matter in the same way that they are applicable to matter. For example an anti-matter dishwasher filled with anti-matter dishwashing liquid meant for hand washing anti-matter dishes would overflow the anti-matter dishwasher with anti-matter suds in the same way that the corresponding regular-matter soap would the corresponding regular dishwasher.

11. On the train I was occupied with mentally running through the details of the upcoming performance in my head, and all the time staring forward at the partition at the end of the seats in front of me, a linoleum panel with a variegated wood pattern.

12. From greek “asumptōtos”, from a “not”, plus sum “together”, and ptōtos “apt to fall”. What are sometimes referred to as “asymptotic lines” or “asymptotically parallel lines” are one of two kinds of non-intersecting lines in hyperbolic geometry.

13. As I noticed that panel in front of me more and more, whenever my attention would be lifted from the thoughts at hand, I also noticed something, some small spot, in the wood pattern. I would notice that, although the wood pattern was not entirely consistent in its repetition, there was one spot in a lighter strip that appeared to be a bit too wide. And then if I looked bit longer I would realize that it was just an expectable inconsistency in the pattern. And then again I was certain it was the result of some sort of vandalism.

14. If, in Euclidean geometry, the parallel postulate could be described as a given line L, and a point, P, not on L, there is only one possible line which can be drawn through P and not intersect L, in hyperbolic geometry there are at least two lines which can be drawn through P that do not also intersect L.

15. At one stop my bag sitting on the seats in front of me slid forward, and I shifted my position to retrieve it. I took the opportunity to lean forward and examine the partition more closely. I immediately saw that there was, in fact, something awry. Someone had scratched three connecting ovals into the surface of the linoleum panel.

16.

The etymology of Versaille is not agreed upon, but (according to Henri Lemoine in Versailles, Cité Royale, which the official website of the town cites) the word might derive from the latin verb versare, meaning “to turn over”.

17. As I sat back into my original seat it remained abundantly apparent that that spot was distinctly not a part of the pattern printed on the panel. I could see the contours of the shape quite clearly – there was no mistaking.

18. In hyperbolic geometry, asymptotic lines, or asymptotically parallel lines, are lines which in one direction infinitely approach each other without intersecting, and the other direction, infinitely diverge.

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