When I was in Junior High, I had a subscription to the "Life Science Library." One of my favorite books was the one called Matter [by Ralph E. Lapp "and the editors of LIFE," Time Inc., 1963]. Besides wonderful presentations on the elements, sub-atomic particles, etc., there was a very intriguing photo at the beginning of a "picture essay" on "surfaces" [pp. 82-83].
| Cognac | .95398 |
| Blue Curaçao | 1.0963 |
| White Creme de Cacao | 1.1229 |
| Parfait Amour | 1.1269 |
| Crème de Menthe | 1.1320 |
| Grenadine | 1.3427 |
California, when he got the idea.
The caption on the picture did not make such a pousse-café sound very sensible or desirable as a drink. It said, "the distinctive surfaces in this bartender's nightmare are very tenuous, since a jolt would blend all the components into a murky mixture." Taking their word for it, that such a drink was just some kind of stunt, I didn't think much more about it -- I wasn't old enough to drink yet anyway. Years went by, and I never heard or noticed anything more about pousse-cafés.
Then in 1990 my wife Jackie started teaching at Princeton. For the first time in my life this not only gave me a chance to visit New York City but to spend a fair amount of time there. (I do like it that I didn't get there until after I had been to world capitals like London, Paris, Rome, Athens, Beirut, Damascus, Cairo, and Tokyo, not to mention Washington D.C. [or Nicosia, Ankara, and Amman] -- one might think that Gotham, or "Moscow on the Hudson," was not much of a priority.) One of places in Manhattan we came to like was the garishly decorated bar in the Tavern on the Green restaurant in Central Park. We never did actually eat at the restaurant, but we stopped at the bar occasionally. Indeed, we had already been there a few times when I noticed a menu, perhaps it was new, for -- guess what -- pousse-cafés.
| Stratus Pousse |
|---|
| Bailey's Creme |
| Midori |
| Crème de Cacao |
| Anisette |
| Grenadine |
| House on Fire |
|---|
| 151 Rum, aflame |
| Midori |
| Crème de Banana |
| Crème de Noyaux |
My favorite drink, however, was the "House on Fire," at right. These were all fairly light and alcoholic liqueurs, so it made for a drink that was both sharp and not very syrupy. It was also rather spectacular, since the rum on top was set on fire, and the waitress had to carry it on a tray from the bar over to our table. This also looked a bit dangerous. It wasn't hard to imagine the flaming rum ending up in someone's lap. When I got home, this also proved to be the most challenging pousse-café to make, since it turned out to be very hard to pour each liqueur on top of the others without mixing them. They must be very close in specific gravity. However, I eventually got the hang of it. But I did leave out the flaming rum part!
| Jelly Bean |
|---|
| Southern Comfort |
| Anisette |
| Grenadine |
With the other drinks, the "Jelly Bean" did actually taste rather like a jelly bean. The Anisette and the Southern Comfort were a good combination. But the last two drinks, the "Port & Starboard" and the "Bandera de Mexico," were mainly for their colors. "Port & Starboard" evidently means the red and green lights that mark the port (red) and starboard (green) sides of ships, and the wingtips of airplanes.
| Port & Starboard |
|---|
| Crème de Menthe |
| Grenadine |
| Bandera de Mexico |
|---|
| Midori |
| Creme |
| Grenadine |
One problem I had making these drinks was finding what to put them in. Almost any kind of regular glass was going to be far too large. Either way too much liqueur would be used, or the layers would be so thin that the colors wouldn't show to much effect. For all I know, there may be a special glass for these things. I didn't pay much attention to the glasses used at the Tavern on the Green. The "picture essay" photo in Matter makes it hard to tell if it is a large glass, just filled up, or a special small one. What I eventually hit upon was a certain kind of tall, thin shot glass, almost twice as tall as a regular shot glass and slightly thinner. This doesn't hold very much, but it may be about as much liqueur as one would want to drink at a sitting, and the layers show to good effect. Tourist gift shops these days seem to the full of shot glasses, usually identified by sight-seeing location, including these tall thin kinds. I especially liked using a shot glass I had bought when my wife Jackie and I went to Death Valley, for the first time, in April 1993. Death Valley is a little out of the way, and not the kind of place I'd want to visit for most of the year. Unfortuately, the glass got away from me while I was pouring a pousse-café a year or so later and broke! Probably not worth another trip, but, come to think of it, we never did get to Scotty's Castle.
The order of the layers for the pousse-cafés listed in the accompanying tables may not be entirely reliable. The last time I made all of these was for a party on New Year's Eve for 1995. I had them all lined up so people could look at them and maybe even try them out. Some did try. Since then I've been drifting away from it. So has the Tavern on the Green. By 1998 they no longer seemed to be offering the drinks. Perhaps a patron got that flaming rum in their lap after all, and the restaurant thought better of it. Or perhaps the bartenders changed and the new ones weren't any good at pouring the drinks. For whatever reason, the special menu is gone.
A lasting effect of this experimentation, however, was my discovery that Blue Curaçao was rather good in Gin & Tonic. Blue Curaçao is mostly tasteless, and the only drink I had ever heard of that contained it was a Rum drink called a "Blue Hawaii." The name of that drink has a nice ring to it, but it was definitely in the category of sweet "tropical" drinks. On the other hand, Gin and Tonic tastes like 7-Up, which the bit of lime with which it is usually served does not correct. I discovered, however, that a dash of Blue Curaçao makes the drink a lot more interesting. The liqueur is not, as I discovered, entirely tasteless. It is made from bitter oranges and definitely has a very faint taste of it. That gives just the right touch to Gin & Tonic. My wife and I have been wondering what to call it. Recently I've discovered that Gin and Blue Curaçao can be called a Blue Moon, but this does not necessarily include the Tonic. So perhaps the drink is a "Blue Moon and Tonic" (without the lime).
The Tavern on the Green closed in bankruptcy in 2009, and all its furnishings were sold. Negotiations continue, and continue, about reopening it. The last few years of its operation, however, we had had difficulty getting into the bar. Once smoking was banned in New York City bars, during the summer the Tavern began seating all bar patrons outdoors, where they could smoke. In the winter, it seemed like every time we went to the restaurant, it was closed for a private function. So when it went into bankruptcy, we actually hasn't been in the bar for some time.
Since that paragraph was written, the Tavern has been remodeled and reopenned. The upstairs bar is gone. I think there are just offices up there. There is a large downstairs bar, but it does not have the same charm. I have not patronized it yet.
Now (2017) I understand that the Tavern has closed again. Of course, after the remodeling, I haven't been back anyway, so I can't feel much loss. But the whole business is depressing.
The store had its own liquor department, and I got interested in their selection of liqueurs -- which ultimately led to my interest in Pousse-Cafés. I did things like putting Crème de Menthe or Crème de Cacao on ice cream as a dessert when I got back the the room I rented behind a garage in Mānoa.
One liqueur that I liked mainly for its color was Blue Curaçao. It didn't have a very strong taste, and I read that it was mainly used for color in a few special drinks, like the "Blue Hawai'i." I don't know that I even had one of those while I was living in Hawai'i. Instead, years later, I began to put a little Blue Curaçao in Gin and Tonic, mainly for the color -- a color as we see at right on this book cover for a Romance novel -- but then I also noticed that it did impart a faint orange flavor, and I came to positively prefer that over plain Gin and Tonic. I began to think of this drink as a "Blue Ruin," borrowing the name from The Eternal Sunshine of the Spotless Mind, where they seemed to be drinking something of the sort.
Eventually I did have a Blue Hawai'i on a memorable occasion, one of the first dates with my wife, when we ate at a Chinese restaurant, Ho Toy's, in Sherman Oaks in 1988. It was done up as a proper Tropical drink, with the little umbrella and everything. Nevertheless, it was some years before I ventured to reproduce the drink for myself. This was after my wife and I had been to Hawai'i for our 16th wedding anniversary in 2007. I came away with a refrigerator magnet with a recipe for the drink. So in the end I used the ingredients from both recipes: 1 oz. cream of coconut, 1 oz. blue curaçao, 2 oz. rum, 2 oz. pineapple juice, and 1 oz. lemon juice. This goes into the blender with two full glasses of ice. All blended together, it makes a couple of full drinks. With the cream of coconut, this makes for a very tasty but certainly very fattening drink. So I only make it occasionally. I do think that it is much like the Blue Hawai'i we had at Ho Toy's.
A curious sequel to this is when my wife and I were back in Hawai'i in 2011. We went down to the sea-side bar in the Royal Hawaiian Hotel in Waikiki for a drink. Looking at the drink menu, there was no Blue Hawai'i. So I asked the waiter if they could make one. He said yes. Naturally, I found this very curious. I think I have figured out what was going on. Wikipedia says that the original drink, invented in 1957 by Harry Yee, head bartender at what is now the Hilton Hawaiian Village in Waikiki, had sour mix in it instead of cream of coconut, and it was over ice instead of blended. Sour mix is yellow; and if you then do not use much Blue Curaçao, you run the danger of producing a green rather than a blue drink. Notice that the refrigerator magnet doesn't mention either sour mix or coconut.
The story seems to be that the sour mix produces a "Blue Hawai'i," while the cream of coconut produces a "Blue Hawaiian." However, I think that if someone is offering up a green drink, they have no business calling it a "blue" anything; and many, many of the images I see on the internet of what is supposed to be a "Blue Hawai'i" (including the photo on the actual Wikipedia page for the "Blue Hawai'i") are actually green, just like the drink they gave us at the Royal Hawaiian.
So, to me a proper Blue Hawai'i will always be a frozen, blended drink with cream of coconut, without the slightest chance it will turn out green -- just don't put too much pineapple or lemon juice (which are also yellow) in it.
The absence of a Blue Hawai'i on the drink menu at the Royal Hawaiian seems of a piece with other disturbing developments in Hawai'i, such as the disappearance (1) of movie theaters from Waikiki, (2) of beach mat zōri, 草履, sandals, or "slippers" ("slippah") in Local speech, and (3) of glass jars containing layers of colored sugar. The beach mat sandals used to be all over the place, but the local company that made them, "Kahili Brand," actually went out of business. I don't know how people get by -- although now I see that one can get Japanese "tatami mat" zōris.
The disappearance of the colored sugar is certainly the result of the end of the industry in Hawai'i. Driving around the Big Island in 1975, there were many burning cane fields. In 2007, none. Fortunately, I have my own stock of beach mat zoris; and my remaining jar of colored sugar, although thrown off the mantel in the Northridge Earthquake (1994), was unbroken. But I am sure that all of this is because of all the haoles (like me) who are overrunning Hawai'i.
With other disappearances, I should also mention (4) the radical remodeling of the International Marketplace on Kalakaua Avenue in Waikiki -- it is now just like a shopping mall -- and (5) the actual demolition in 2019 of the little shopping center on Kaiulani Avene that in my day was called "King's Alley" and later "King's Village." It was like a little walk-in city, with a narrow street winding up between shops. I am reminded of the Two Rodeo Drive shopping center in Beverly Hills, which also has such a little pedestrian street going up into it.
In 1974 I saw a lot of King's Alley since my first wife waitressed for a while in a restaurant at the top of the building. I would meet her late when her shift was over and we would go home together to Mānoa on late busses. Now there is a highrise hotel there, like so many others in Waikiki. I don't know if its bar has a Blue Hawai'i.
Finally, I should mention (6) the Wailana Coffee House, which was on Ala Moana Blvd in Waikiki, as we see in the photo, with the venerable Ilikai Hotel in the background, familiar from the opening credits of the also venerable Hawaii Five-O TV series [1968-1980]. The Wailana was venerable enough, having opened in 1949.
My experience with the Wailana was limited, but it began memorably when my first wife took me there for a late night snack in 1973. I don't know how many times I would have gone there over the years, but my last visit was memorable in its own right.
On my last time in Hawai'i, in 2011, I got up the first morning at the Marriott in Waikiki and took a taxi to the Wailana for breakfast. That was all fine, but my plan was to walk back to the hotel. The problem was then gout attacks in both knees, probably brought on by dehydration on the plane flight. So the walk was painful, especially stepping off of curbs. This persuaded me that I should be taking some medication for the gout, which I have since then.
The family that ran the Wailana actually owns the building it was in, but they decided that the expensive renovations needed for the restaurant were too much, so they closed it in 2019. Not the "lost our lease" excuse in this case. One family member had actually been a cook in the kitchen. Another sad business for the Old Hawai'i. Well, there is an IHOP a few doors down, so next time I can at least eat in the same neighborhood again.Blue Hawai'i
When I was first living in Hawai'i in 1972, I would walk home from the University up East Mānoa Road and stop at the Safeway that used to be there to buy such small amounts of groceries that I needed -- I ate most of my meals on campus.
This I compared with a recipe from my drink book, The Complete Bartender [Robyn M. Feller, Berkley Books, 1990, p.115]. The recipe there, for a "Blue Hawaiian," called for 1 oz. light rum, 2 oz. pineapple juice, 1 oz. blue curaçao, and 1 oz. cream of coconut. The two recipes differed in that the magnet included some lemon juice, and the book included cream of coconut. The "cream of coconut" was the Coco López brand that I had been seeing in stores for years but had never used for anything -- I had not made my own Piña Coladas, which I expect is the most common use for the product -- the coconut gave the drink a texture that also reminds me of the ruffled fabric of the dress on the book cover of the Romance novel above.
What they brought back was a drink that was actually green. God knows what they had put in it. Green Hawai'i? It tasted all right, but it also manifestly did not have cream of coconut in it.
| County | Borough | Post Office |
|---|---|---|
| New York | Manhattan | New York |
| The Bronx | The Bronx | The Bronx |
| Kings | Brooklyn | Brooklyn |
| Queens | Queens | Long Island City |
| Flushing | ||
| Jamaica | ||
| Far Rockaway | ||
| Floral Park | ||
| Richmond | Staten Island | Staten Island |
The chart at right sorts out these complications. The Counties and "Boroughs" coincide territorially but in three cases have different names. The Borough of Staten Island sometimes used to be called "Richmond," like the County. The postal addresses match the names of the Boroughs except for Manhattan and Queens. It is in Queens that the most interesting variation is found, since there are five different postal addresses for the County/Borough. Most of Queens looks divided, about evenly, between Flushing and Jamaica, with Long Island City, Far Rockaway, and Floral Park on the edges. There is in fact little of Floral Park in Queens, because Floral Park addresses straddle the boundary between Queens and adjacent Nassau County -- so someone living in "Floral Park" may or may not be a resident of the City of New York.
The Bronx is the only Borough where the name of the Borough, the County, and the Post Office are all the same. Also, uniquely and inexplicably, it is always used with the definite article. A discussion of this kind of usage can be found in relation to the Ukraine, where the use of the article in English seems to puzzle and alarm Ukrainians.
While the City of New York has its own Mayor and City Council, each Borough has its own government, with a Borough President and a Borough Hall.
 |
| American Radiator Building, 1924, in foreground, from Bryant Park, New York City, September 2017 |
|---|
New York City, along with its fame as a financial, entertainment, and fashion center, is well known for its insane rent control laws and the abandoned buildings and blighted neighborhoods (Harlem, the South Bronx, and Bedford-Stuyvesant) that have resulted. On Staten Island, more conservative than the rest of the city, there has been talk about leaving the City.
Comparably complicated is the City of Greater London. This consists of 32 Boroughs plus the Mediaeval City of London itself, which is equal in status to all the rest put together, which constitute the County of London.
Each Borough has its own Council, although there is some variation in what these are called. One of the Boroughs, Westminster, is also a City, but it does not otherwise seem to be institutionally distinguished. Westminster not only contains the Houses of Parliament (Westminster Palace) but also what is traditionally regarded as the geographical center of London, at Charing Cross.
London originally grew up surrounded by the County of Middlesex. As London grew, there were various complications and confusions of overlapping authority, until the County of Middlesex itself was ended in 1965, with all of its territory falling to London or some other surrounding counties. Aware of places like Middlesex County, New Jersey, travelers may wonder why there isn't a Middlesex surviving in England.
After all this, Greater London is slightly larger in population than New York City, with the former topping 8.6 million in 2015, and the latter 8.5.
The East-West Center at the When I was graduate student at UH from 1972-1974, I spent a great deal of time in the Cafeteria that was in the basement of the administrative building of the Center, Jefferson Hall (which, I think, may have been renamed). It was the nicest place to eat at the University. Since the cafeteria has now been eliminated and the space broken up into conference rooms, what it was like back then deserves to be remembered.
It was the nicest place on campus to eat. Cafeterias usually aren't like that. Cafeterias in basements usually are the worst. The East-West Center cafeteria, however, although in the basement, was open all along one side of the building to a sunken garden. Mostly lawn, actually, but with a fair number of plants around it. Wedding parties seemed to turn up regularly to have pictures taken. And it was a big place. I can't remember it being full, though it was quite busy at lunch. Most of the time I remember being there, in the afternoon, it was pretty quiet. Those are the times I would just sit reading. That is where I first read and studied, hot off the presses, Leonard Nelson's Progress and Regress in Philosophy. That is where I sat reading The East-West Center, especially the Cafeteria, was certainly the kind of place where such meetings were possible. At right we see Gandhi sitting at his spinning wheel. He thought that encouraging everyone to spin and make their own clothes would make India independent of British industry. Unfortunately, he didn't realize that this would only perpetuate India in her poverty, since hand spinning is not very productive. His exortation, "Live simply that others may simple live," although still a blueprint to some, embodied a terrible misunderstanding: If everyone lives in poverty, like Gandhi, then many people died of famine, disease, overwork, etc. An industrial scale increase in productivity means a mass market and abundant wealth for everyone. India since independence has not really taken Gandhi's ideas in that respect seriously, but it has perpetuated poverty anyway through efforts to apply socialism. Nevertheless, Gandhi's ideas about non-violence are both historically, morally, and politically important.
Like most cafeterias, the food at the East-West Center cafeteria wasn't very good. I tried their tempura once and, not knowing any better, figured that tempura was awful. It wasn't until several year later I learned that tempura wasn't supposed to end up soaked in cooking oil! I might have learned sooner, but Japanese food wasn't the fashion in Honolulu in the early 1970's. My first wife and I only ate at a Japanese restaurant once while I was living in Honolulu. Chinese food was what was popular then and there. Sometimes it seemed like there was a Chinese restaurant on every street corner. My first wife ate sushi and Hawaiian raw fish a lot, but she tended to buy them in packages by the checkout counter at the supermarket (now I would wonder how fresh the fish was). I never made it to a "sushi bar" until I was back in Los Angeles from Texas for a while in 1980, by which time sushi had become very popular.
On the other hand, the cafeteria did have great teriburgers. They left the hamburger patties soaking in the teriyaki sauce, and I have never had such good ones. When my wife Jackie and I were back in Hawai'i in 1988, and I discovered to my horror that the East-West Center cafeteria had been closed, all we could do was go eat at the Student Union cafeteria. There all they did was dip the patty in the teriyaki sauce before serving it. No comparison.
The best thing about the East-West Center cafeteria, however, was making friends. I wasn't the only graduate student hanging out there. Some of the best friends I made were Cathy Barale and John Gregory. Cathy was, I was given to understand, the first non-Chinese Teaching Assistant in the Chinese Department at UH, despite being a robust blond Chicagoan. She had already lived in Taiwan and, obviously, had quite good Chinese. Her stories were wonderful, and she had a great sense of humor. As someone devoted to China might be, she wasn't all too keen on Japan; and whenever she had a story involving some run-in with Japanese, however innocent or even humorous, she usually said it was "Nanking all over again." Since Honolulu often nearly seemed overrun with Japanese tourists, even back before Japanese investors began buying up the place, there were a number of occasions when we were out on the town that it was "Nanking all over again" (e.g. the crowds outside the Duty Free Shop in the middle of Waikiki).
John, on the other hand, was one of my fellow grad students in the Philosophy Department; but his specialty was Chinese Philosophy, so it often happened that he and Cathy would get talking about things Chinese. Once I was in on it, they ended up explaining to me how Chinese characters were structured (radical & phonetic) and how to use a Chinese dictionary. It was as good as taking a class. Although I still have no facility at it, I never have failed to find a Chinese character that I wanted to look up, though I did find it easier to use (gasp!) Japanese character dictionaries to do that.
Cathy and John both ended up as witnesses at the wedding for my first marriage, signing the Marriage Certificate. Unfortunately, getting married meant I spent less and less time at the East-West Center cafeteria, and I began to drift out of the old circle. My last year in Honolulu, while I was teaching part-time for Chaminade College, I was rarely even on campus and began to seriously lose touch with my old friends. Moving to Texas in 1975, I lost contact altogether.
In retrospect, this was very foolish, but at the time, being a young fool, I did not realize that life was so short and friends so precious -- although now I have also discovered that the drifting away and estrangement of friends can happen even when one exerts some care to stop it. The last thing I heard was more than ten years ago when I asked John DeFrancis, one of the distinguished Professors of Chinese at UH, after I had written him about a new book he had published (The Chinese Language, Fact and Fantasy, University of Hawaii Press, 1986), what he knew about where Cathy had gone. He said he thought she was in China. No surprise about that.
Concern for the fate of some other old friends at the East-West Center has weighed on my mind. Strangely enough, there was a large group of Afghanis studying there, and they were a regular feature of the East-West Center cafeteria. They were very good humored and friendly, and since I had lived in the Middle East and studied Persian, which they knew, we had something in common, so far from home, as it were. When I first saw them, there was one guy who looked like a real scion of the Central Asian conquerors. He was tall, very dark, wiry, and had a scarred face. He did not look like someone to mess with. Before long, however, I discovered that he was the mildest sort of person, and his appearance was totally disarmed by a rather high pitched voice. All of them, however, would have been back in Afghanistan before the terrible events of the pro-communist coup and then the Soviet invasion. Almost twenty years of war against the Russians, and civil war, and then a lunatic fringe government of Islāmic fundamentalists have made Afghanistan a very different place from the country that, in the early 70's, had the reputation of a great place to go to smoke hashish without getting hassled or arrested. Hippy heaven to a much more familiar Third World hell-on-earth. I hope that my Afghani friends from Hawai'i managed to settle down to a better life elsewhere.
Now those days of books, friends, and restfully looking out to the rain of Mānoa (Ua Tuahine) falling on garden and hillside, in dear Hawai'i Nei, are long gone.
On the eve of Memorial Day in 1981, there was a terrible flash flood that occurred right in the middle of Austin, Among the businesses devastated on that stretch of Lamar was a hippy health food store, the original The police really didn't know what to do. There hardly seemed a way to get out to the stranded man without getting carried away by the water first. So there was a bit of standing around. Then another car pulled up, and another guy got out. Just another spectator. But after looking around, the guy went back to his car, opened the truck, and got out a wet suit and a rope. He put on the wet suit, handed one end of the rope to a cop, jumped into the water, and swam out to the stranded man. He got the man in tow and swam back to the high ground. On emerging from the water, as Robert related it, the guy actually said, "It's Miller time." I never heard anything else about this event, or the guy, so he must have just driven off into the darkness (such as it was). I still like to use this story in my ethics classes as an example of actions "above and beyond the call of duty."
Isaac Asimov (1920-1992), beloved, departed, and sorely missed, once said, "The truth is that I love mathematics and mathematics is completely indifferent to me" ["Exclamation Point!" in From Earth to Heaven, Discus Books/Avon, 1972, p. 101]. I might say the same of myself, though I am not sure that I am enough interested in mathematics to really say "love." "Like" might be more like it. I like mathematics more than it likes me. I suspect it even liked Issac Asimov better than me.
I was not doing well in my junior high school math classes, actually getting C's and D's, when something surprising happened. It was the Space Race Era, and science education was being pushed. They wanted to start promising students early in algebra. The test they gave to identify the promising students happened to identify, of all things, me. So I went from C's and D's in regular math to getting B's in algebra and geometry, right up into high school.
There came a point, however, where my promise began to flag. I was back to getting C's in high school Algebra III and Trigonometry. The algebra class seemed like a particular disaster, with the teacher writing unintelligible stuff on the blackboard and then complaining that we were all stupid for not understanding it. I'm not sure that is the point of teaching. Trigonometry was better, and a lot more interesting, but I wasn't cutting it for some reason and gave up trying to go further in math. The next step would have been calculus.
My overall grades in high school were not so great (I think I graduated with a 2.6 or something), so it didn't seem like I would be headed for a top flight college. I was already thinking about the University of New Mexico anyway, since I wanted then to go into their archaeology program. It wasn't, I didn't think, as picky as the University of California. Then another surprising thing happened. My SAT scores came in to the school counselor, who was rather astonished at the result. No more than I was, actually. I had gotten a 681 on the Verbal part and 738 on the Mathematical. Both of these were in high percentiles for all high school senior boys, and I think that the math score was over the 90th. Suddenly I was University of California material, since in those days one could be admitted to any UC campus on the strength of grades OR on the strength of SAT scores. Although I ended up going to New Mexico for a year anyway, I had applied and was admitted to Berkeley, and then came back to UCLA for my Sophomore year.
I never did take any college math. Whatever that 738 scored showed, it wasn't anything that meshed with mathematics most of the ways I had seen it taught. None of the math books I ever saw explained anything in ways I found interesting or intelligible. They seemed to jump directly from the trival and obvious to the advanced and opaque, without much in the way of discussion of anything. Nor was I brilliant or interested enough to do it by myself. So I took a pass. I even had the same trouble when I tried taking a logic class.
By the time I took the GRE, it was my verbal score that soared far above 700, while the math score had sunk down so far in the 600's as to be somewhere in the 80 percentiles. That hardly was surprising. More distressing was the fact that, starting graduate school in philosophy, I was going to have to take a symbolic logic class. Mathophobia time.
Oddly enough, I did rather well. I even ended up as a logic Teaching Assistant, both at the University of Hawaii and the University of Texas. At Texas I also noticed something else: I actually seemed to remember things like algebra better than most of my friends. And I enjoyed the chapters about mathematics when I began reading collections of Isaac Asimov's science essays. Asimov seemed interested in about the same way I was in understanding and playing with relatively simple mathematical principles. I soon discovered that Kepler's Equations were about my speed; and in the era of the first pocket calculators, the late 70's, it was possible to use logarithms and trig functions without the dreadful and stupfiying mediation of the log and trig tables. Slide rules were history, and I could even put away the abacus that I had used with the log and trig tables in high school.
Gauss I was not. But I had some fun. Playing with Kepler's equations I came to particularly like conic sections. The way they had always been taught to me, in rectangular coordinates with different equations for ellipses, parabolas, and hyperbolas, had always been especially opaque; but then I discovered that in polar coordinates, a single equation would do for all conic sections. This was much more elegant and revealing (Newton had derived such an equation from his equation for the force of gravity); and it seemed of a piece with my math education that I had never been taught anything of the sort.
The most that ever came of such play was the following derivation. While I was living near the University of Texas campus in early 1981, I used to spend time hanging out in the Texas Union, which had been closed for renovation most of my earlier years in Austin. Sitting in the Union and making notes, I decided to try and derive as many properties of conic sections as I could just from the definition of eccentricity. The following 63 lines are no big deal, but they did accomplish something I always wanted but never saw in math books: Every step of logic without any "fill in the gaps" exhortations or expectations. Spinoza tried to do philosophy like geometry. I don't think that is particularly helpful. But I think it is certainly helpful to do mathematics that way -- when it can be: Since Gödel, even mathematics cannot be entirely formalistic. Perhaps that is part of the trouble I have with higher mathematics.
The East-West Center Cafeteria
University of Hawai'i is a research institution that is really separate from the University as such, but all the buildings are adjacent to each other on essentially the same campus, and no casual examination would reveal that they are not all the same operation. Much the same thing can be seen at the University of Texas, where the Lyndon Baines Johnson Presidential Library, and its attendant research center, is not part of the University but is at the University and hardly seems like less than an extension of it.
Passing through the bushes at the back of the garden, one would go down into the bed of Mānoa Stream, which usually had running water in it, often quite a lot. That is where I had my first kiss with my first wife. Up behind the stream was the hillside of the St. Louis Heights ridge that enclosed the Mānoa Valley on the south side. The photo at right actually shows the back of Jefferson Hall. The arches along the bottom of the building were right outside the cafeteria, so the view from within was the grassy scene shown. Mānoa Stream would be out of the picture down to the right. Sitting near the windows in the cafeteria, the hillside beyond was itself plainly visible. In the winter, such as it was, the hillside would even be brown for a while. Otherwise it was green. Of course, even in winter, it usually wasn't cold enough for the doors to be closed. It was always just screen doors that closed off one whole side of the long room.
Mahātmā Gandhi's Autobiography. As I was actually doing that one day, there was an Indian women sitting across from me. At one point she spoke up to say that she had known Gandhi herself and still had letters from him. Since he didn't believe in wasting paper, he wrote his letters on the inside of envelopes.
The Whole Foods Flood
Texas. There had been floods like that in Austin before, but none that bad since near the turn of the century. Flooding on the main river than runs through Austin, the Colorado River (of Texas, not the one of Colorado, Utah, Arizona, and California), had been taken care of in the Depression when a series of dams were built along it, including the dam that makes Town Lake in the middle of the city. But a flood had occurred earlier on Waller Creek, which runs down the east edge of the original city. The flood in 1981 was along Shoal Creek, on the west edge of the original city. There was some speculation afterwards that the urbanization of the Austin area contributed to the flood potential, since water runs off streets easier than off open country. That may have played a part, but it was hard to see the storm itself without expecting something bad to happen, wherever it was going to be.
I was living at the time not far from Shoal Creek, on 26th Street, near were the street ended, at the top of a cliff above Lamar Boulevard and Shoal Creek itself. That evening a strong thunderstorm moved in. Nothing unusual in May, when I had seen, since moving to Texas in 1975, some of the most violent weather of my life -- I even had a hail stone break a brake light on my car (though that was small potatoes compared to what hail can do). I had run an errand to a friend's house during the evening, and it was already raining hard. Very hard. That kept up and got worse after I got home. Soon I had never seen it rain any harder, and the flashes of lightning became so frequent that they literally left no darkness between them. It was a bright day of arc light. I settled down to watch television. The night was getting on, and the storm kept up. Then the television station went off the air. I think all of them did. Then the power went out. I looked around a bit, and nothing unusual, except for the rain, seemed to be going on in my neighborhood, so I went to bed.
The next morning I awoke to the news of what had happened during the night. Just a couple hundred of feet from me, below the cliff, Shoal Creek had risen and flooded over Lamar Boulevard for much of its length through the central city. People had died, including the son of one of my professors, mostly by trying to drive across the rising water and then getting swept away. Much of the area was park and green space, but water had run at least six feet deep through one business district along Lamar south of 15th Street. On that Memorial Day, clear, sunny, and warm, crowds of people were inspecting the damage and marvelling at the high water marks on the buildings. It hardly seemed possible. A number of car dealerships down along 5th and 6th Streets had even had a lot of their stock washed out into Town Lake. It was so strange. Apart from the deaths, the mud, and the cars in the Lake, everything otherwise just seemed like an ordinary Spring day. Just a block away, as I had been during the night, one would never have known of any disaster. Later in the day, I even went to a picnic that some friends had previously organized.
Whole Foods Market. The store was wiped out. They cleaned up and rebuilt, even surviving a couple more floods, though not as bad, later. When I was in Austin in 1993 the store still had a display on the outside, showing how high the water had risen in the different floods. Soon they were opening new stores. Later they were expanding outside of Texas, buying out some other health food chains. Now, after they bought the Mrs. Gooch's stores in California in 1993, they even have a store about a mile from where I live in Los Angeles. Kind of fascinating, to be there when the business was nearly strangled in the cradle, then have it spread all over the country. Since one of the owners is a Libertarian, it is fitting that the story should end up being like something out of Ayn Rand. On my last trip to Austin, in 2000, I discovered that the original Whole Foods Market had moved down the street, to higher ground, in a brand new building. The original location now has a clothing store.
The strangest story of the flood, however, was one told by a couple of my own friends, Robert Daniel and Mike Rogers. They were out doing a bit of drinking that night. Long after the flood had started, but unaware of what was happening, they headed back to Robert's house, driving west along 9th Street from downtown. They didn't notice anything unusual (apart from the thunderstorm and all) until they got to Lamar. At 9th, Lamar was actually above water, but north of there, the street dipped down into the flooded area. What they noticed at first were police cars parked at the intersection. When they stopped and looked around, they could see what was happening. They got to survey the scene. It must have been dramatic enough. More dramatic, however, was a man hanging onto the sign in the parking lot of a 7 Eleven store at the corner of Lamar and 10th. He had been caught in his car and then managed to get out and get onto the sign. The police didn't know quite what to do. The rushing water was many feet deep around the sign, even as the heavy rain and lightning continued. They were not prepared for rapid water rescues.
Conic Sections
| SOME PROPERTIES OF CONIC SECTIONS |
|---|
 A conic section is a locus of points at a fixed ratio, called the "eccentricity" e, from a point, the "focus," and a line, the "directrix." The propositions begin with the definition of the eccentricity. The points on the curve are a distance r, the "radius," from the focus, and a distance h from the directrix. The eccentricity is the ratio of r to h. The distance from the focus to the directrix is g. An eccentricity equal to 0 defines a circle, between 0 and 1 an ellipse, equal to 1 a parabola, and larger than 1 a hyperbola. Particularly elegant, simple, or important equations are marked with an asterisk "*". The simplest equation of all, for all conic sections, is line *15 ( r = d - ex ), which is unusual in that it mixes rectangular (x) with polar (r) coordinates.
"Periapsis" is the shortest radius for any conic section. In astronomy, closest approach to the Earth is called "perigee," closest approach to the Sun is "perihelion," and closest approach to the Moon is "periselene." Finally, the sixth diagram, below, for lines 49 and 55, shows the "semi-minor axis" b, which is the perpendicular from the center to the curve, line f, which is the radius that intersects the semi-minor axis, and xf , the x coordinate of the center, which of course is equal to c. The aphapsis, Q, is the longest radius in an ellipse. In astronomy, the farthest point in an orbit around the Earth is called "apogee," farthest point in an orbit around the Sun is "aphelion," and farthest point in an orbit around the Moon is "aposelene." While a, b, c, and Q are all defined for ellipses, they also have physical meaning for hyperbolas. Hyperbolas can be thought of as ellipses where the major axis is negative and the minor axis is imaginary. The physical meaning of all the equations about conic sections pays off in the Equations for Kepler's Laws, where the same notation for the properties of the conics is used.
Copyright (c) 1999 Kelley L. Ross, Ph.D. All Rights Reserved |
In the Proceedings of the Friesian School I have been writing, Asimov-like, about some of the mathematical things that I have come across. The Separation Formula in Relativity, the Golden Ratio, Imaginary Numbers, and Imaginary Powers are a few of the things that I have found intriguing enough to want to study, understand better, and write about. I never did get very far into calculus, but then it seemed to raise as many questions as I ever found answered.
With Asimov gone, lately I've found interesting and useful mathematical ideas in The Penguin Dictionary of Curious and Interesting Geometry by David Wells [Penguin, 1991] and The Most Beautiful Mathematical Formulas (Les Plus Belles Formules Mathématiques) by Lionel Salem, Frédéric Testard, and Coralie Salem, translated by James D. Wuest [John Wiley & Sons, 1992].
The second diagram, for lines 2 and 3, shows the angle 
that the radius makes with g, and the x coordinate, which is the segment of g from the focus to the perpendicular dropped from the curve.
The third diagram, for lines 10 and 11, shows the "semi-latus rectum" d, that radius where 
The fourth diagram, for lines 16 and 17, shows the "periapsis" q, or "closest approach," that radius where 
The fifth diagram, for lines 30 and 31, shows several other dimensions used with ellipses.
The furthest distance of the curve from the focus is the "aphapsis" Q. The two quantities, q and Q add up to the "major axis." The major axis is used less often as a dimension than half its length, the "semi-major axis" a. The distance from the center of the major axis, which is also the center of the ellipse, to the focus is c.
