The Last Rose of Summer

The autumn starts on 9/22 this year. This is the definition from astronomy. Traditionally & meteorologically it starts roughly around September 1 or Labor Day in Canada & US. So 8/31 is the last day of summer. This reminds me a lovely song “The Last Rose of Summer”. Although the last rose of summer does not necessary falls on the last day of summer, it conveys the same message that the

summer will soon be over & the last rose will wither & fade away---sad emotion. The song is from an old Irish air “The Groves of Blarney”. John Stevenson adapted this tune on “The Last Rose of Summer”, a poem by Thomas Moore. Since then this song becomes very popular. In fact, Flotow used this song in his opera Martha & appears several times in different acts. Martha is a comic opera, a love story of two boring ladies & two farmers who hire them as servants. When farmer, Lionel fell in love with the leading lady Harriet, she gave the rose she wore to him & sang the Last Rose of Summer. After that, the two ladies fled & returned to the court. Lionel was so distressed, he sang a famous aria “Ach! So fromm” (恍如夢中). The opera is not very long & generally considered to be a light opera. The ending is a happy one --- they marry & live happily ever after (有情人终成眷屬). Just before the curtain falls, they sing once again “The Last Rose of Summer”.

Though there are many arias in Martha, only the above two are really famous. The opera is very unique in some way, as Germans consider it a German opera, French consider it a French opera, Italians consider it an Italian opera. Of course English think it is an English opera with setting in Scotland with Irish Last Rose of Summer. Flotow is a German receiving music training in France. He composed Martha in German, but the original script is in French. The opera was translated into Italian with high quality that most Italians think it is from Donnizetti. Especially, the aria “Ach! So fromm” is translated into Italian “M’appari tutt’amor”. It is this title aria made Martha well known in the opera world. I think European Union (EU) needs a lot of people like Flotow to unite the Europe. Something similar happens to Dvorak’s symphony #9, “From the New World”, 2nd movement. American people think it is very American. But most people from Czech & Slovakia have no doubt about it. It sounds so Bohemian that they become home sick immediately. I haven’t found anything like this among China, Korea & Japan. The one close to it are the songs we all familiar with, 送別 & 憶兒時. 送別 becomes “旅愁”in Japan. 憶兒時 becomes 故鄉の老家. Japanese think they are Japanese songs. Most Chinese have no doubt that they are Chinese songs. But the truth is that both of them are American folk songs. 送別 was composed by John P. Ordway (1824-1880) with title “Dreaming of Home & Mother. 憶兒時 was composed by W.S. Hays (1837-1907) with title "My Dear Old Sunny Home”. The peculiar thing is that not many American people know Ordway & Hays, let alone these two songs.

The following are some YouTube links that you can listen to the songs I mentioned above:

The Last Rose of Summer

http://www.youtube.com/watch?v=3nc55QYn970

Ach! So Fromm, sing in German by Wunderlich

https://www.youtube.com/watch?v=PEyG3xG3rOM

M’appari tutt’amor, sing in Italian by Pavarotti and Lanza

https://www.youtube.com/watch?v=ypDQoiryv1Q

http://www.youtube.com/watch?v=4yvC7A2YoMs&feature=related

Dreaming of Home & Mother

http://www.youtube.com/watch?v=KWSP0dD8gnM&feature=related

My Dear Old Sunny Home

http://www.youtube.com/watch?v=9l9wA_Ho-v0

The above link switches authors of music (tune) & lyrics.

http://www.pdmusic.org/hays.html;

Move the screen to 1871 and click My Dear Old Sunny Home

Dvorak's Going Home

http://www.youtube.com/watch?v=FiEuoE9sViA

Some photos from Hubble Space are spectacular. You almost think our home is in the deep space of our cosmos. But at the last moment, the distintive blue marble shows up from the corner & it is our Earth, an almost ocean sphere. The Earth is truly our home.

Slide Rules

I just cleaned the garage & found a good old slide rule I used to use in our Taida’s day. It is a Hemmi 153 for EE. After so many years, I can barely remember the scales & functions. Most of you use Hemmi 255, also for EE.

For some reason, I seldom used it in my graduate classes in the US, although I was still an EE major. The discipline of EE consists of many fields such as communication, power, control system, computer & logic, circuit & network, electronics, solid state physics, etc. Most of these fields stress on theory & application. The numerical calculation is minimal. In other words, due to lack of case study or field application, the calculation is fairly limited & so the use of slide rule is rare. Compare to law & MBA programs, our EE seems less exciting & lack of colorful or hot discussion. I spent half day to review my good old slide rule & would like to share some of my finding. Of course, most of us knew these long time ago. Here are the scales I found in Hemmi 153:

L: Logarithm

K: Cube

A: Square

A,B: Multiply, Divide

C,D,CI: Multiply, Divide, Proportion

T: Tangent

GTheta: Gudermanian Angle for Sinh on T scale & Tanh on P scale

Theta: Angle of Trigonometry, 360 degrees in a circle

RTheta: Radian Angle of Theta, 2 pi in a circle

P,Q,Q’: Sin, Cos & Hypotenuse of Right Triangle

LL3, LL2, LL1: log log scale for exponential functions

The operation of the slide rule is by sliding center bar and finding the answer using various scales. So the operation is basically Addition & Subtraction in nature. However, if the scale is calibrated in a logarithmic fashion, then the multiplication becomes addition & division becomes subtraction. That is exactly what scale A,B,C,D & CI do. In fact, the scale L is calibrated from 0 to 10 in equal spacing. As to the calculation of exponential functions, it takes one more log to convert exponent to multiply. In LL3, LL2 & LL1, the scale is calibrated in log log fashion, so the calculations of exponent is converted to addition, a slide rule operation. GTheta is Gudermanian Angle for finding Sinh on T scale & Tanh on P scale. It is not obvious why hyperbolic functions have anything to do with Tangent & Square functions. I think the key is how GTheta is defined. Most electrical engineers are not really interested in the definition of GTheta. All we care is getting Sinh from T scale & Tanh from P scale. As a matter of fact, the graph of Sinh looks like Tan & Tanh looks like Sin in the range of principal values.

Nowadays we don’t see slide rules except the places like museums. This is one example that technology changes the way we calculate, and so the way we live. You might ask why. In 1972, HP introduced HP-35 Electronic Calculator. It has 35 buttons (so called HP-35) with four functions, trigonometric, logarithmic functions, square root & exponential functions. The accuracy of the calculation is 10 significant digits. Since it can perform all the functions of the slide rules & do them more accurately (10 significant vs 3 or 4 digits in slide rules) and efficiently (much faster), it sent the slide rules into oblivion. From then on, slide rules faded away like old soldiers & books of math tables disappeared in no time. In 1972, I worked for Mostek, a spin out of Texas Instrument. Mostek supplied three ROMs for HP-35. I had the chance to see the complete binary code of the algorithms & its architecture. The processor operates fetch, store, branch, add & shift with four registers. Each register has 56 bits, organized as 14x4, ie 14 digits in BCD. The internal register calculations are 14 digits and the accuracy is 10 digits. It is a very primitive but compact processor dedicated just for scientific calculations. The four functions are calculated with add & shift. Logarithm is calculated using Sequential Table Lookup (log 2, log 1.1, log 1.01 & log 1.001). For example, log 30 is converted to a series of numbers as follows:

Log 10*3 = log 10* 2*1.5 = log 10*2*1.1*1.36

= log 10*2*1.1*1.1*1.1*1.01*1.01

= Log 10 +log 2 + 3*log1.1 + 2*log 1.01.

Since log10=1, log 2, log 1.1, log 1.01 are the constants store in ROM, you just look them up & add to get the correct answer. The method seems cumbersome. But the processor is fast enough to get the most results within 3 seconds.

Trigonometric functions are calculated by Rotation Method (CORDIC) with Sequential Table Lookup (arctan 1, arctan 0.1, arctan 0.01, arctan 0.001 and arctan 0.0001). The angles correspond to 45°, 5.71°, 0.57°, 0.06° and 0.01°. For example, Tan 52° is converted to Tan (45+5.71+ 0.57 + 0.57 + 0.06 + 0.06 + 0.01 + 0.01 + 0.01). For each rotation, use the formula we learned from Analytic Geometry:

X’ = xcosA - ysinA

Y’ = xsinA + ycosA

The values of sin & cos of the angles 45° to 0.01° are stored in ROM.

The final result Tan 52° = X’/Y’. Sin52° = Y’/SQRT(X’²+Y’²) & Cos52° = X’/SQRT(X’²+Y’²).

Exponential function exp(x) can be obtained similar to logarithmic function. Convert x to m0*c0 + m1*c1 + m2*c2 + m3* c3 + m4*c4. The constants in ROM c0, c1, c2, c3, & c4 are the values of ln10, ln 2, ln 1.1, ln 1.01, ln 1.001, ln 1.0001. So exp(x)= exp(m0*c0 + m1*c1 + m2*c2 + m3* c3 + m4*c4) = 10^m0 * 2^m1 * 1.1^m2 * 1.01^m3 * 1.001^m4, can be calculated by add & shift operations.

Some of us might have chance to take a course called Numerical Analysis in graduate school. It is considered part of the computer science curriculum. Alas, it didn’t mention anything that I found in HP-35. One thing I did know at that time why HP didn’t use Infinite Series, it is the speed of the convergence. It is hard to find infinite series converges fast enough for the slow processor in 1972.

作文與命運

Sometime ago in our classmate email communication, we talked about the composition in our joint entrance examination & how important it was to our future. Here is another example. I read a book “小脚與西服” several years ago. It was written by Natasha Chang who is the grandniece of 張幼儀, the first wife of 徐志摩. This is a very interesting book which describes the whole thing from the interviews she conducted with 張幼儀. Several years ago, Taiwan produced a TV Show--人間四月天--, a very good show that traces the love affair of 徐志摩. In小脚與西服, it mentioned 張嘉璈, the brother of 張幼儀, went to 杭州第一中学 to see the condition of the school. While he examined the work of the students, he was so impressed by 徐志摩's composition, he made a decision to arrange the marriage between 徐志摩 & his sister 張幼儀. After this, we all know the rest of the story: unhappy marriage, divorce, can’t marry 林徽因 as she refrained, found another lover 陸小曼, financial difficulty, … , airplane accident to end his life. This is the hindsight: If it were 林長民 (father of 林徽因) instead of 張嘉璈who read the composition, the future & fate of 徐志摩 would have been completely different. It would have been a perfect marriage 徐志摩+林徽因 & the Chinese literature might have been added one brilliant chapter. Anyway, this is just another example of the importance of composition to one’s future.

PS1: 林長民 was well known, literally & politically and became a very good friend of 徐志摩. While 林長民 stayed in London, his daughter 林徽因 lived with him & attended college in London. 徐志摩 went to Cambridge & had chances to meet her. And so the love affair flourished. 張幼儀 moved to Cambridge but couldn’t salvage the marriage as 徐志摩 divorced her in no time. She later moved to Germany & eventually returned to China.

Ps2: The title of TV series “人間四月天“ is from a poem by 林徽因: “你是人間四月天”. She majored in architecture and well verse in literature. Her father-in-law is 梁啓超. Her father is 林長民, the cousin of 林覺民, one of 黄花崗七＋二烈士.

Gleaners

I bought an old book recently in a book sale of local library. It is Balanchine’s Complete Stories of the Great Ballets (Doubleday & Company, Inc. 1954). I read Giselle & Swan Lake. Somehow it reminded me that I read the same text somewhere before. I happened to have a copy of “笆蕾舞與樂曲的故事", published in 1958 by 拾穗雜誌. It dawns on me that the latter is the translation from the Balanchine’s book. Anyway I am sure most of us knew 拾穗雜誌 when we were in high school & college. It was a pretty high quality monthly magazine. Beside this book, 拾穗雜誌 also published “西洋歌剧的故事”and “交响樂的故事”around 1956. After 1957, 吳心柳 founded “音樂雜誌 and published it for several years. These two monthly magazines were fairly influential in the last five years of 1950’s. 吳心柳, also known as 張继高, wrote some other books like 樂府春秋 and 從精緻到完美 etc. I learned a lot from these two magazines when I was in school. Time goes fast, they are all gone & passed away. It is quite nostalgic when I reread some of these books. After 1960, 文星雜誌 & 皇冠雜誌 entered the center stage. That was the time of 李敖 & 瓊瑤. Somehow 李敖 didn’t like 瓊瑤 & attacked her novel ”窗外”. Anyway, that is another story. Go back to 拾穗雜誌, its cover is the famous painting by Jean Francois Millet, a French impressionist. Millet was a painter fond of the peasant scene. His paintings show the relations between nature & human being. They give you a feeling of hardworking peasants toiling their labors & still find harmony with the nature. Usually the background is the golden sunset or blue sky with patchy clouds couple with a remote chapel with its steeple. It has a profound effect to the viewers. I heard that his several paintings are now on display in Taipei, including his two most famous paintings: The Gleaners (拾穗) & The Angelus (晚祷). I saw these two original paintings at Musee d’Orsay in Paris in 1986. The museum was used to be a railway station. It was just converted to a museum at that time. Several years later, I purchased the reproduction copies in Palo Alto downtown at $16 apiece. I hang them in my family room since then. The Gleaner has three women in the foreground, one looks like mother in the center, the one on the left looks like her daughter and the woman on the right looks a little bit older and can’t bent comfortably. The background is a field with harvest activities and golden sky. The golden field extends remotely to the sky and forms a uniform color---穗野共長天一色.. You watch this painting & realize there are still some poor people live on the grains left by the harvest. Perhaps they have some children to feed at home & so they have to work hard to get by. You feel very sorry for them and hope their children will eventually get good education & get out of the situation. I remember during 1970’s, there was an engineering weekly magazine in Silicon Valley ran a contest matching famous painting with engineering activities. The Gleaner won the contest with title: “Boy, if those guys in Texas Instruments find out this is the way we grow semiconductor chips, ……”

The Angelus is even more famous than the Gleaners. This painting shows a peasant couple takes time off in the field to say prayers before going home. It is after sunset, it is getting dark but the sky is still glowing with golden color. The most prominent & moving scene is the remote church steeple. It gives you the ambient of bell ringing & you seem to hear it. At this moment, you really feel & understand---勞動神聖. Long time ago (1936), 開明書店 published a book by夏丏尊, title 平屋雜文. In this book, there is one article “米萊的晚鐘”. 夏丏尊 said “信仰, 勞動, 恋愛, 這三者融和一致的生活才是我們的理想生活. He then extended the argument that the women need to labor physically or mentally in order to gain economic-independent status in the society. I wouldn’t go that far but I like his imagination. This painting gives me a feeling of peace, harmony & assurance of the future. It is interesting 夏丏尊 used 晚鐘 instead of 晚祷. That means he focused more on the church steeple than the prayer.

Ps: 夏丏尊 also translated the well-known book 愛的教育 (by Edmondo Amicis). There are several versions of translation published after him. However, I think his version is the best. 夏丏尊 was a teacher & educator & I always found passions in his work & writing.

Midsummer Night's Dream

This is the midsummer time, time for vacation & relax. It is also a time for dream, a midsummer night's dream. Shakespeare wrote a lot of tragedies, but they are too heavy for most people. It is this Midsummer Night's Dream makes him a great playwright of comedy. Since its first performance in 1596, it continues to capture people's imagination & attention. The plot of the play is a mixture of mytholody, fairly tale, romance, jealousy, mischief, etc. After all, it is like a dream. It does show that our love affairs tend to go astray, go blind pursuit & wake up to the reality eventually. It may be the most popular play of Shakespeare. They are numerous music, opera & ballet performed every year based on this play. The most popular one is Mendelssohn's Incidental music of Midsummer Night's Dream. He composed the overture of it when he was 17 years old. He eventually finished the other part of the music 16 years later by the request of German Kaiser. The most famous pieces are the following:

1. Overture

http://www.youtube.com/watch?v=4h1MGAlkqno&feature=related

2. Scherzo

http://www.youtube.com/watch?v=3dLhSZLIpvA&feature=related

3. Nocturne

http://www.youtube.com/watch?v=-QElxEypehc&feature=related

4. Wedding March

http://www.youtube.com/watch?v=sVjyLbTItmw&feature=related

Wedding March is traditionally played in a wedding ceremony after the couple make the vow & parade down the aisle. It was started by Queen Victoria in 1858 by marrying her eldest daughter. From then on, it becomes a tradition.

Mendelssohn was a German with Jewish blood. However, he converted to a Lutheran christian. Even with this conversion, he was still shuned by people like Wagner & Hitler's Nazis. Most of the discrimination occurred after his death. He is generally considered the most fortunate composer in history. He came from a rich jewish family, have happy family & marriage. He was a child prodigy & a good painter, got acquantance with Gothe, Humboldt, Liszt, Chopin, German Kaiser and Queen Victoria etc. All in all, he lead a very happy life. No wonder his music is gay, lively & merry with romantic mood. If you listen to his Violin Concerto & Italian Symphony, you will surely appreciate his romantic quality. He also selflessly revived the music of Bach & Schubert to a new height.

He was very close to his sister Fanny. He died due to heart-broken one month after her death . His another sister Rebecca married Dirichlet, a great German mathematician. Most of us are familiar with Dirichlet, a person credited with modern definition of Function. It is interesting to know that Dirichlet's doctoral advisors were Simeon Poisson & Joseph Fourier, two heavy weights in electromagnetics.

Poisson's equation with no charge is Laplace's equation. We all know that they can be deduced from Maxwell's equations. But in history, it was the reverse procedure. Maxwell got to know all these equations & summed up with his great four equations. Fourier developed Fourier series & integral via his study on heat transfer. He worked under Napoleon on the expedition to Egypt. It was a failure campaign with some valuable bonus to the history. It was during this expedition that French army discovered Rosetta Stone. It is displayed in British Museum these days. The Rosetta Stone is a piece of rock that contains the same text with three different languages: hieroglyphic, Demotic (ancient Egyptian) & Greek. It is surely an open-sesame to understand Egyptian hieroglyphics which was undecidered at that time. It was a breakthrough event in history. I was in the British Museum several years ago & touched the stone to feel the history, a unique experience. Napoleon was graduated from the French academy of artillary. He was an expert of gun warfare. Fourier at that time was solving heat problems of French guns in the field of Egypt. He developed the famous Fourier series & the concept of representing any non periodic function with Fourier series. His work increased the efficiency of guns, influenced the campaign & the mathematics. As we all know, Napoleon was defeated in Egypt not by British army, but by British navy, lord Nelson in Battle of the Nile. Nowaday we go to Trafalgal square in London, a statue high up in the column is (you guess it right) Nelson. French army shouldn't feel bad on Egyptian expedition & Fourier certainly must be proud of his work. He also discovered in 1824 the so-called GreenHouse Effect which becomes a very important subject these days.