0 & 1

Natural number is for counting. Long time ago, people didn't count nothing. So there is no concept of zero. George Gamow wrote a famous book “1, 2, 3…Infinity”. He said our ancestors used to count 1, 2 & 3. If it was more than 3, it was many and definitely no concept of 0. But when we have 4 birds and sold 2, we have 2 left. How many are left when we sell the final 2? We will say I don’t have any, I don’t count. But that is just awkward. We can say we own nothing & call nothing 0(ZERO). So finally we have 0 left. Natural number can have 0 or not depending on whom you talk to. But it seems the natural number is not so natural after all. The counting of year in the human civilization has been a mess. The lack of concept 0 & its notation led to confusion. People think it is natural to count from 1. After all, why is there a need to count nothing? This creates no problem when we count things that are not divisible like men. For example, if every man own 10 beads, ten men will have 10x10=100 beads. But when we count thing that is divisible like year (divisible to days), we encounter something awkward. In second year (year 2), we try to count how many days passed from the beginning of year 1 when the day is February 1. We have to calculate with (2-1) x 365 + 31. But what happen if it is the first year we try to calculate? We get (1-1) x 365 + 31. Here (1-1) is a concept of zero but we just don’t have the notation 0 to represent it. Without the concept of 0 also led to the absence of AD 0 in Christian Calendar. So the years between 1 BC & AD 1 is not 1-(-1) = 2, but only 1. If Chinese people count the year starting from 黃帝, 2697 BC, the conversion of 2010 is 2010-(-2697)=4707. But 2010 BC will be -2010-(-2697) + 1= 687+1= 688, assuming the first Chinese year is year 1. The reason of this discrepancy is the gap between 1 BC & 1 AD, Zero. This kind of awkwardness happens often. For example, we count day 1 of the week, 星期一…六 and on Sunday, we call it 日. Subconsciously, it means 0 and we call the starting day of the week 星期日 (Sunday). So 星期一 of the week is actually not the first day of the week. Subconsciously people treat 星期日 as 星期零 (not 星期七). The way we count the age went through the same confusion. Chinese count the infant age 1 when it is born. Eventually they found the problem & called it 虛歲. The notation of the counting without 0 is 1, 2,…,10. The last number 10 is unnatural since it uses digit 0 after 1 & it contains 2 digits. What is the definition of Decade, Century & Millennium? Since there is no zero, you have to define a decade from 1 to 10, a century 1 to 100 & millennium from 1 to 1000. But what happened to the world when Millennium came several years ago? To aggravate the situation, the so-called Y2K problem played havoc to the computer world. What was the reason behind all these problems? Just look at the number from 1999 to 2000. There are four digits that flip. But from 2000 to 2001, there is only one digit flips. It is the counting without 0! There were two camps of people in celebrating Millennium, one for 2000 & one for 2001. Since there is no 0 AD, the new millennium must be 2001. Guess what? Most people went ahead to celebrate on 1/1/2000, the last year of the old millennium, not the beginning of the new millennium. Why caused the shift? People already get used to the concept of zero in counting. Also it is just awkward to count 1001 to 2000 as a millennium. So now we have an embarrassing situation, the first millennium is from 1 to 999, only 999 years. The third millennium is from 2000 to 2999, a perfect 1000 years. This year is 2010, it is the beginning of a new decade, not the last year of the old decade.

The dawning of the computer age creates the necessity of programming languages. In digital world we use 2, 8 or 16 base system ie binary, octal & hex base system. We all order the digits starting from 0. Here we skip the 4 base system since we think it is trivial. As a matter of fact, this is what our ancestors used, 1,2,3…Infinity. 0,1,2,3 are the 4 digits for the 4-based system. All computers count from 0 to the last digit of the base & wrap around to 10. Zero is the lowest unsigned integer value, one of the most fundamental types in programming and hardware design. In computer science, zero is thus often used as the base case for many kinds of numerical recursions. Proofs and other sorts of mathematical reasoning in computer science often begin with zero. For these reasons, in computer science it is not unusual to number from zero rather than one. There have been so many kinds of languages like car companies in the early 20th century. Eventually it settles down to just a few and C language becomes the most popular one used in the software industry. The most powerful feature in C is the Pointer. It is basically a kind of Array Indexing. All indexing in C starts from 0. You define Array[40], but can only use Array[0..39]. If you get out of bound, the compiler will flag it as an error. It becomes very natural for most programmers to think things starting from 0 instead of 1. It is ironical that most hardware engineers don’t like C language. They rather like to use BASIC in their work. I know some principal engineers hate C language just because they never really feel comfortable or grasp the zero-based indexing, especially the concept of Pointers.

The indivisibility of 0 is another subject warrants separate discussion. It is interesting to note that 0 & infinity form two ends of the counting scale, one left, one right. It is not surprising that indivisibility of 0 relates to the infinity. Without the concept of zero & infinity, there will be no concept of Limit & so there will be no Calculus. Zero & Infinity are two pillars that lead to the Limit & Calculus which make our world a much better place to live.

PS0: One of the most natural number is e. When e is expressed in infinite series, it starts from index 0:
Summation of 1/n!(n=0…infinity). It is the same in sin(x) & cos(x) & Taylor series.

PS1: Some time ago (1971) when a group of philosophers tried to celebrate the 2,400th birthday of Plato (428 BC-348 BC). They got the problem as they couldn't get the consensus as to pick 1971 or 1972 for celebration. Logically, it should be 1972, not 1971 since there is no AD 0.

PS2: We have 元年, 元旦 or 正月. It sounds as if people vaguely have the concept of 0 & try to distinguish it from 1.

PS3: Have you ever heard of "雙簧管效應"? It is called "OBOE", ie Offset By One Error. This happens very often in our life, for example 植樹問題, year counting (19xx as 20th century), column count in a building & Loop index error that crashes computers.

地球的私語---如泣如訴的樂章

The Climate Change Conference was held in Copenhagen, Denmark. It was a distress to see constant quarrels between countries, especially the developed & developing countries. The moral question is “Who Speaks for Earth?”

On August 20th and September 5th, 1977, two identical spacecraft Voyager I & Voyager II were launched to the space. Inside each spacecraft, there is a gold plated record containing the valuable information that someday some one in the outer space may find it meaningful. After exploring Jupiter, Saturn, Uranus & Neptune, Voyager I left the solar system & wandered into the remote universe. Just at the edge of the solar system, Voyager I took a last photo. In the photo, we find a Tiny Blue Dot. This is the Earth, our home. Voyager I will be near a star in the Ophiuchus constellation (蛇夫座) in about 40,000 years. It is very unlikely that it will ever be accidentally encountered. If they are ever found by an alien species, it will most likely be far in the future, and thus the gold record is best seen as a time capsule or a symbolic statement rather than a serious attempt to communicate with extraterrestrial life. In September 2003, I bought a book “Murmurs of Earth” from a book sale in Palo Alto library. It contains two CDs, the copy of the gold record sent to the outer space with the Voyagers. The second CD contains 27 pieces of music. Among them there are 3 by Bach, 2 by Beethoven & 1 by Mozart. The last piece of the music in the record is Cavatina, 5th movement of String Quartet No. 13, Opus 130, by Beethoven. This music is really deep in emotion, mostly sad & murmuring. It is like 默默許願, 細細傾訴, 切切私語, 如泣如訴. Ann Druyan who worked on the project had the following philosophical comment:

Sadness alone can’t define the Cavatina. Strains of hope run through it as well, and something of the serenity of a man who has endured suffering and come to terms with existence perceived without illusion. It may be that these ambiguities make for an appropriate conclusion to the Voyager record. We who are living the drama of human life on Earth do not know what measure of sadness or hope is appropriate to our existence. We don not know whether we are living a tragedy or a comedy or a great adventure.

It is most appropriate that this piece of music concludes the space journey with the meaning of the Golden Record: Murmurs of Earth. We may listen to the Cavatina in the following link:
http://www.youtube.com/watch?v=fosTnfoMj30

It was performed by the famous American String Quartet in Taipei, March 21 (Spring Equinox), 2008, at 台北國立藝術大学(Taipei National University of the Arts). Perhaps some of our classmates in Taipei attended this concert in 2008. The original copy in the golden record was performed by the Budapest String Quartet.

After listening to Cavatina three times, I found the following poem fits very closely to the mood:
低 眉 信 手 續 續 彈, 絃 絃 掩 抑 声 声 思, 小 絃 切 切 如 私 語, 說 盡 心 中 無 限 事.
When some species in the outer space find this record million years later, it will be 同 是 天 涯 淪 落 人, 相 逢 何 必 曾 相 識.

PS0: Both poems are from 琵琶行 by 白居易.

PS1: “Who Speaks for Earth” is the last episode of the Cosmos, A Personal Voyage by Carl Sagen (1980). It is timely to watch it again if we really concern the outcome of the Copenhagen Conference.
The DVD of Episode 13 of the Cosmos: "Who Speaks for Earth?" can be checked out from most of the local  libraries.

冬之旅 與 林登樹

Winterreise (Winter Journey, 冬之旅) is a set of famous poems written by Wilhelm Muller. Schubert composed a song cycle based on it. The most famous one is Lindenbaum, 菩提樹. It is very popular in Taiwan & Japan. Almost every school kid knows the tune. However, 怪事年年有. Lately someone found that Linden is not 菩提樹, it is 椴樹. There is a famous street Unter den Linden in Berlin, Germany. It is named after the linden trees lining the boulevard. In German folklore, the linden tree is the "tree lovers." Some famous buildings line along the street are Berlin State Opera, German Historical Museum, Humboldt University, Frederick the Great Statue. I heard that 龍應台女士 used to gather some leaves of Linden on this street (while she taught in Germany) and tried to verify whether it is really 菩提樹. She found that they are not the same trees. Their leaves look alike but not identical. Linden has 齒狀邊緣 but 菩提樹 has smooth edge. To people who sing 菩提樹 for so many years, it is like a terrible betrayal. To add to the confusion, Japanese also call it 菩提樹. Perhaps the person just translated this from the Japanese text or some one in China might just goof in translation. The error was made long time ago but should we stick to it? 椴樹 may be ideal for botany, but too bookish or serious for music and literature. I suggest we just change 菩提樹 to 林登樹 per criteria of 信,達,雅. After all, Schubert's Lindenbaum really has nothing to do with 菩提 or Buddhism. The following link shows the pictures of the leaves of 菩提樹 and 林登樹.

http://interp.sow.tw/b6_nature/botany/dicotyledoneae/bot_dicot_peepultree.htm

PS: 龍應台女士曾當過台北文化局局長. She was well known in 1980’s in Taiwan for her 野火集. We may not be familiar with her books since we were so busy in picking cups for our hot chocolate (per AJ’s pps) at that time. Her new book “大江大海, 1949” opens a pandora box & says “以失敗者的下一代為榮”. It sounds like an interesting & moving(emotional & touching) book especially for those whose parents moved to Taiwan from mainland after 1949. 龍女士 was raised & educated in Taiwan (苗栗與台南). Her 祖籍 is 湖南衡山 . She used to think she was 湖南人. Until one day she was in 衡山, nobody there thought she was 湖南人 since she knew so little about 衡山 & 湖南. Now she considers herself a 新台灣人.

Mockingbird

It is approaching late autumn, the liquid amber & Chinese pistache start dropping their leaves and the yards & streets are turning to gold & red in color. It is the time of year again people prepare for Thanksgiving holidays & find time for meditation. I found one thing unusual this year. Several mockingbirds are still around & sing various calls in the early morning. They sound like a bunch of mischievous & naughty boys who chatter & make fun. They are especially vocal in the early morning & late afternoon. In the neighborhood, other notable birds are robins, ravens & blue jays. The robins always feed on the yard in pair. They have orange chest & are easily identified. Sometime you pass by them, they sort of freeze & pretend they are not birds at all. The ravens basically are crows, noisy & aggressive. They are big birds & are not welcomed most of the time. Blue jays are vivid blue in color & can be very noisy. They sound like calling 賊 in the daytime. Perhaps this is the reason why they are called Jay (jay & 賊 同音, just for fun). When the autumn is fast passing by, most birds sort of fade away by migration. Except those mockingbirds, they seem still happy to hang around here. One morning I found young one tangled with the golf net & couldn’t get out of it. Its mother & father hovered around to call each other for help. After a few minutes, they were not successful freeing it. I tried to be helpful. I untangled the little bird & found that this little bird had a hard time to fly. So I put it in an open box with some water. There was nothing I can do except sitting nearby to see what is going on. This was the day I heard more mockingbird calls than any other days in my life. Lunchtime was coming & I had to leave. I let the evolution ran its course. Miraculously, they all disappeared after I finished the lunch. For some reason, I felt very happy for the rest of the day. I even tried to whistle like a mockingbird. Perhaps this is the adage: 日行一善 or 助人(鳥)為快樂之本.

When it comes to 助人為快樂之本, it reminds me of 青年守則. We all remember that we had to recite or sing the song 青年守則 every morning while we were in elementary school. I didn’t like to memorize it & was not particularily impressed by it. However, when I get older, I really appreciate #10, 助人為快樂之本 & #12, 有恒為成功之本. In the past few years, I especially valued #4, 信義為立業之本 & #5, 和平為處世之本. If most countries in the world follow #5, there will be few wars on earth. If most people in Wall Street (including CEOs & MBAs) follow #4, there will be no Charles Ponzi, Enron, Bernard Madoff & all the financial mess in this country. The next two items I like are #11, 學問為濟世之本 & #9, 整潔為強身之本.

While we are talking about birds, do you still remember a good old radio program in 1960's, 早晨的公園? This program was anchored by 潘啟元. If you tuned to this program, you would hear all sort of birds singing different tunes. When you had to get up early & head to school, you wouldn’t appreciate it. I visited Taipei once in 1975. I got wakened up by this program & I didn’t have to go to school. I felt so relaxed & really appreciated those birds that make the world a nice place to live.

The last thing about mockingbird is that famous book “To Kill a Mockingbird”. Most of us have watched this movie in Taiwan with title "梅崗城的故事" as the story occurred in a town called Maycomb. It is story about a lawyer Atticus Finch (finch is also a bird) defended a black man in the case of raping a white woman. Why is the book called “To Kill a Mockingbird”? Here is the quote from some source: 'when Atticus, having given his children air-rifles for Christmas, allows their Uncle Jack to teach them to shoot. Atticus warns them that, although they can "shoot all the bluejays they want", they must remember that "it's a sin to kill a mockingbird”. Confused, Scout (the girl who narrated the story) approaches her neighbor Miss Maudie, who explains that mockingbirds never harm other living creatures. She points out that mockingbirds simply provide pleasure with their songs, saying, "They don't do one thing but sing their hearts out for us. "To kill a mockingbird" is to kill that which is innocent and harmless—like Tom Robinson (the black man).'

秋之旅

Autumn is here again, the season of harvesting, of thanksgiving, of bird’s migration, of preparation for bear’s hibernation, of meditation for some people. But is it real the season for a journey? I was in one Chinese bookstore last week. I encountered a book 秋之頌, by 余光中. I thought the poet had the mood to say something about autumn. It turns out to be a book in praise of 梁實秋. I have a lot of respect to Mr. 梁, but this is not the one I am interested at the moment. I did find a book by Hermann Hesse (赫塞), a Nobel Laureate of Literature, 1946. The title of the short novel is 秋之旅 (1907). 赫塞的短篇小說 有一種獨特的風格, 意境深遠, 今人回味無窮. 這小說並沒有特別指出發生在秋天. 但重頭到尾給你一種秋氣肅穆的感覺. 秋之旅 描寫一位青年在流浪和懷鄉之間徘徊的心靈. 重遊舊地的落寞和昔日情人相遇的感傷, 給人有一種人生虛幻無常又孤獨哀傷的感受. 原文是德文, 看翻譯文學最重要的是翻譯者的功力. 中譯本衹有四十頁, 分成下面幾章: 渡湖, 投宿, 風暴, 往事, 靜寂的村落, 清晨動身, 伊爾根貝克, 尤琍, 霧. 比起 Muller/Schubert 的冬之旅, 赫塞的這篇小說比較輕鬆, 並沒有給你一種失意, 失戀, 落魄而近乎絕望的感受. 秋之旅給你一種孤獨,流浪,虛幻無常的感覺, 但不是痛苦到一种近乎絕望的悲情. 也許這就是秋天和冬天的不同吧!

寫到這裹, 想起赫塞的另一篇小說 “青春,美麗的青春" (1916). 我在1965年看到沉櫻(本名陳瑛)女士翻譯的. 譯文流暢, 非常傳神,令人回味不已. 這篇小說大約也是四十來頁. 描寫一個青年冀圖開拓命運而又懷念家鄉,憧憬浪漫的愛情而又希求安定歸宿的故事. 在一個暑假裡,他回到家鄉和親人相敘,其間發生了一些親情,友情,愛情的故事. 這小說我看過三次 (age 20’s, 40’a & 60’s), 每次感受都不一樣. 想起我們剛大學畢業,申請到國外大學的 admission or scholarship. 負笈彼邦以前,每一個都是青年冀圖開拓命運而又懷念家鄉. 在暑假時回家一趟,看到親人故舊,無不感到溫馨,同時憧憬浪漫自由而又希求安定歸宿. 所以讀起這篇小說更是容易感到共嗚. 同時這也是感嘆夏日之逝去,迎來绮麗的秋之旅.

Nobel Prizes

All Nobel Laureates were announced. They are all American except two, one Romanian German, one Israeli. This is the age of American as far as the Nobel Prize is concerned. Half of the American winners are immigrants, naturalized citizens. Obama is a black horse to win the Peace Prize, a surprise to most people in the world. Even he himself doesn't think he deserves it. Peace Prize is very subjective & political. Some people even interpret this as an award to the American People who after all elected him as the president & so have a foresight & promise to the peace in the future.

Now move to the other front. One resident of Mountain View in California won the Physics Prize. Charles Kao is an Electrical Engineer. He is awarded for his work on Fiber Optics. The other two persons share the prize are also Electrical Engineers who worked on Charge Coupled Devices (CCD)that makes modern digital camera possible. The only bad thing is that Kao worked on fiber optics in 1965 & he got the award a little bit late (44 years later) since he already develops some kind of Alzheimer's disease. It is pretty hard for engineers to get Nobel Prize mainly because they usually focus on the application side of the scientific discovery or invention. OSI is the open model used in the communication & network industry. It consists of seven layers: physical, link, network, transport, session, presentation & application. Only the physical layer relates to the device physics and can be a potential candidate of Nobel Prize. In this Internet age, the influence of the Ethernet protocol (link layer) is immense. But it is not in the radar scope of the Nobel Prize. I spent almost two years working on Fibre Channel Storage Network. My works were in the link, network & transport layers & had very little to do with the physical layer. Charles Kao got the prize mainly due to his research on the physical layer. Depending on your career goal, you have to focus on something, after all you only got 24 hours a day. My engineering work on fibre channel has a lot to do with the communication protocols & software. Anyway, I got four patents out of my work.

It is not uncommon for a person to wait 30 years to get the Nobel Prize. For patent, it is not that bad, but still takes time. You may have to wait three years or more to get patent granted. In our Taida days, we used to hear some brilliant classmates set the goal to get Nobel Prize in some distant future. Time flies, the distant future is now. The first one I know is 許貞雄. He was my good old classmate in high school & major in physics. He got his Ph.D from University of Wisconsin & went to Stony Brook to follow 楊振寧 for post-doctoral research. He didn’t stay long before he went back to Taiwan. I asked him about the whole thing several years later. Here is what he said: “Dr. Young is so deep (in thinking or something else) that I lost all my confidence as a research fellow of physics.” He opted to teach in 清華大學 for the rest of his life. In our EE Dept, the most notable candidates are 李純儀 & Amo, both of them are visible & vocal. Lately we haven’t heard anything from 李純儀 about his ambition. However, Amo is still pursuing. We should proudly cheer: “Carry on, Dr. Amo.”

Moon & Rusalka

中秋節 of 2009 falls on October 3. The temperature hovered around 60 degree on the day & I haven’t seen the moon so bright, so round & so shining for some time. I checked the luner calendar, it said 已丑中秋節. I don’t know how many people still use or follow 天干地支 counting in China. It takes 60 years to reach a cycle & restart. So when someone says 一甲子, he means 60 years. I have no idea why our ancesters used this system. Perhaps people at that time in average only lived to 60 years of age. Otherwise it will be confusing when some one say 甲午年. It may be 1894 or 1834. Think about it, we are all over 60 years old. How about 壬午年, it may be 1942 or 2002. As a matter of fact, our history book lists all these terms: 戊戌政變, 甲午战争, 辛亥革命, 庚子賠款 etc. It is nice to know that the events occur in that year. But the problem is that you really don’t know how it relates to 公元 or how many years between those events. You have to do some conversion or cross reference. I do have an algorithm that converts BC or AD to 天干地支. It is as follows:

十 天干：甲乙丙丁戊已庚辛壬癸 (index 0-9)
十二 地支: 子丑寅卯辰巳午未申酉戌亥 (index 0-11)

For AD, use (Year –4) & the following calculation:
(1972 - 4) mod (10) ≡ 8，所以天干是“壬”；
(1972 - 4) mod (12) ≡ 0，所以地支是“子”。
So 1972 is (8,0) 壬子
Same conversion leads 1942: 壬午

For year from 1 to 4, it is:
4: 甲子
3: 癸亥
2: 壬戌
1: 辛酉

For BC, it is more complicate & I will reserve this for some other time. Let’s get back to a soft side of our life. Moon to most of us is romantic. It shines on us, no talking, no complain, no excuse. No wonder some poet like 李白 & others ran the imagination to the wild. Here are some examples:

暮從碧山下, 山月隨人歸.
举杯邀明月, 对影成三人.
我歌月俳佪, 我舞影零乱.
暫伴月將影, 行樂須及春.
星隨平野闊, 月湧大江流.
霧溼樓台, 月迷津渡.
明月如霜, 好風如水.
明月幾時有, 把酒问青天.
沙上珏禽池上暝, 雲破月來花弄影.
海上生明月, 天涯共此時.
露從今月白,月是故鄉明.
明月松間照,清泉石上流.
深林人不知,明月來相照.
月落烏啼箱霜滿天

But the most famous & appropriate to 中秋節 is:
人有悲欢離合, 月有陰晴圓缺, 此事古難全.
但願人長久, 千里共嬋娟.

梁弘志 wrote a song “但願人長久”using 苏東坡 的水調歌頭 as the lyrics. It becomes very popular since 1980’s. On the western front, Dvorak composed “Song to the Moon” in opera Rusalka. It is one of the most well-known song dedicated to the moon. 歌 詞 傷 感, 期 待 而 無 耐, 冷 艶 而 淒 婉. 最 後 一 句 是 近 乎 绝 望 的 呼 喊. Rusalka is a water sprite, who seeks love with human beings that proves to be tragic. Here is the lyric in Czech & its verbatim translation: (* is repeated verse)

Mesiku na nebi hlubokem--------------O moon up in the deep sky
Svetlo tvé daleko vidi,------------------Your light sees distant places
Po svete bloudis sirokém, --------------You travel round the wide world
Divas se v pribytky lidi. ----------------You look into people’s houses
--------------------------------------*You travel round the wide world
--------------------------------------*You look into people’s houses

Mesicku, postuj chvili------------------ O, moon, stay for a moment
Reckni mi, kde je muj mily------------- Tell me where is my love!
----------------------------------------*O, moon, stay for a moment
-------------------------------------*Tell me, oh, tell me where is my love!

Rekni mu, stribmy mesicku, --Tell him please, silver moon in the sky,
Me ze jej objima rame, -----------------That I embrace him,
Aby si alespon chvilicku----------That he should for at least a while …
Vzpomenul ve sneni na mne ------------… remember his dreams!
-----------------------------------*That he should for at least a while …
--------------------------------------*… remember his dreams!

Zasvet mu do daleka -------------------Light up his distant place,
Rekni mu, rekni m kdo tu nan ceka!---Tell him, who waits here!
----------------------------------------*Light up his distant place,
------------------------------------*Tell him, oh, tell him who waits here!

mneli duse lidska sni -------------------If he dreams of me, …
At'se tou vzpominkou vzbudi! ----------… may this memory waken him!
Mesicku, nezhasni, nezhasni!---O, moon, don’t disappear, don’t go!

Here we found some striking similarity between eastern & western version that shows human feeling is universal. If we look at the first stanza of the song, it is 轉 朱 閣, 低 綺 户, 照 無 眠. The second & third stanzas are sort of like 不 應 有 恨, 何 事 偏 向 別 時 圓.. The fourth stanza is 人 有 悲 欢 離 合, 月 有 陰 晴 圓 缺, 此 事 古 難 全. The last stanza is equivalent to 但 願 人 長 久, 千 里 共 嬋 娟..

The following video clip is Rusalka performed by Lucia Popp, a Slovak soprano. She is ideal for singing Czech opera.
http://www.youtube.com/watch?v=4qxi-sYUT9s

PS:
Dvorak (1841-1904) is a Czech composer. His most famous works are Symphony from the New World, Cello Concerto, “American” String Quartet & Slavonic Dances.