Chopin & Schumann

Both Chopin & Schumann were born in 1810 & so this year, 2010, is their two hundredth anniversary of birth, a bicentennial celebration. It is proper & fitting to say something about them.

Chopin is popular in his piano music. Sometime he is called 鋼琴詩人. In fact he composed no symphonies, operas & very little orchestral work. His virtuoso is in the piano works. He is considered the most non-German of all great composers. Chopin had an interesting encounter with George Sand. 桑女士 , a woman frequently wore man’s clothes & indeed intended to act like a man. She wrote many novels quite popular at her time. Chopin was under her spell until he died. The fortunate things coming out of this perhaps was some of his brilliant piano works dedicated to her. Chopin’s famous music form, etude, is unique. The etude (練習曲) is a piano work written for students. However some of them are very good & romantic. Chopin Etude op.10 no.3, Tristesse (Sadness, 離別曲) is one of them. The title’ Tristesse’ was added later by publisher because of Chopin’s nostalgic mood to his homeland. His another romantic piano piece is Andante Spianato in G, Opus 22. I never heard this one in Taiwan. I heard it the first time on radio several years ago. This is one of his most romantic piano works. There are several movies from Hollywood for Chopin. “A Song to Remember” (中文 title: 一曲難忘, 1945) is one of them. I have seen VHS video released for this movie, but can’t find it on DVD, not in Netflix either. I did find some video clips from YouTube.

Chopin Met Liszt in Paris, a clip from ‘A Song to Remember’
www.youtube.com/watch?v=4aDnNJ6aEWc&feature=related

A clip from ‘A Song to Remember’, a performance staged by George Sand & Franz Liszt. It was supposed to be played by Liszt. Instead Chopin played in the dark, a surprise to the audiences.
http://www.youtube.com/watch?v=BM-KQc2lJdM

Chopin: Etude op.10 no.3, Tristesse (Sadness, 離別曲), played by Kempf
http://www.youtube.com/watch?v=1TR-i4r1BtM

Chopin: Andante Spianato played by Rubinstein
https://www.youtube.com/watch?v=l39ZIkyvOJ0

Schumann is considered to be the most romantic of the Romantics. We often heard some of his tunes in the school, for example, the happy peasant 快樂的農夫, tramarel(夢幻曲) etc. He is unique among most composers that he also wrote music critic, encouraged & supported the late comers. His writings about music (in high quality) appeared mostly in the Neue Zeitschrift für Musik ("The New Journal for Music"), a publication that he jointly founded. His romantic encounter with Clara Wick was well known. His most popular works include Symphony #1(Spring), #3(Rhenish), Carnaval, many songs, piano work Traumerei, Fantasy in C, concerto in A minor etc.

As a person, Schumann is much more controlled & dedicated to what he wants & what he think is right. He pursued Clara with zeal & dedication is far more respected than the weak & meek behavior of Chopin’s dealing with George Sand. Schumann was also quick in recognition of a genius & gave the approval. Instead Chopin seemed in failure to recognize the merit of Schumann’s work ‘Carnaval’. Hollywood likes romantic story. The movie ‘Sound of Love’ (1947) is for Robert & Clara Schumann. Same as ‘A Song to Remember’, I couldn’t find it in Netflix. However, I did find it in YouTube. Some of the music mentioned above can be found in the following links:

Happy Peasant (快樂的農夫), a tune we heard in the elementary school
http://www.youtube.com/watch?v=HKmpQjjQOBA&feature=related

The beginning of the movie 'Song of Love'
Ironically, the opening theme is the piano concerto #1 of Franz Liszt, not Schumann.
http://www.youtube.com/watch?v=OP_iU-lcZ5Y&feature=related

Widmung (Dedication) from ‘Song of Love’
Here we listen to two versions of Widmung, the original one from Schumann & arranged version by Liszt. It seemed Clara didn’t like the Liszt version at all.
http://www.youtube.com/watch?v=H3eOggcKLqk

Waltz by Brahms (for the introduction to the next link ‘Brahms & Clara’)
This waltz is one of the most romantic works by Brahms.
http://www.youtube.com/watch?v=TJcoaIeH3GI&feature=related

Brahms & Clara from ‘Song of Love’
The melody of Brahms’s waltz showed up at 1:54 & Brahms proposed to marry Clara. However, the fate intervened at 4:18. Widmung, the song Schumann dedicated to Clara showed up. Brahms realized that was the end of the affair, an affair to remember. This is the most romantic & poetic moment of the movie. (By the way, from 6:35 to 9:06 is the famous Piano Concerto in A Minor by Schumann. 6:35-7:27 is 1st movement, 7:28-9:06 is 3rd movement.)
http://www.youtube.com/watch?v=vm-Zh0R6nMY&feature=related

Traumerei & the end of the movie 'Song of Love'
http://www.youtube.com/watch?v=V35e5MNjLJI&feature=related

The above links of 'Song of Love' are not available due to the copyright issue on YouTube.

Horowitz plays Schumann Traumerei (夢幻曲) in Moscow
http://www.youtube.com/watch?v=qq7ncjhSqtk&feature=related

Widmung (Dedication, Liszt’s version) played by Lang Lang
http://www.youtube.com/watch?v=GBdffJHZ2LM

PS: Year from 1809 to 1813 was a fantastic period of Romantic Music. Here is the chronicle (the magnificent six were all born within this period):
1809: Felix Mendelssohn (date: 2/3), 抒情聖手
1810: Frederic Chopin (3/1), 鋼琴詩人
1810: Robert Schumann (6/8), music composer & critic, 嚴肅而又浪漫的作曲家
1811: Franz Liszt (10/22), 鋼琴鬼才
1813: Richard Wagner (5/22), 樂劇之王
1813: Giuseppe Verdi (10/9), 歌劇之王

For some reason, it skipped 1812. Perhaps the year was reserved for Napoleon Bonaparte. He was not born in that year, however, he invaded Russia, an important historical event.

1949

“1949 by 龍應台” is a book for the unknown people get crossfire between wars. It is the most neglected part of the human history. If you read books about the modern history, you always have a kind of feeling that something must be or must have been missing. So a prudent reader searches more information from different sources in order to verify the facts. If you try to find more information about the common people in the history book, you will be very disappointed. Most of the story about the common people instead can be found in novels or magazines. But the stories in novels or magazines are not rigorous in verifying facts. To most Chinese, the modern history (1945-2010) is a giant jigsaw puzzle. You don’t trust the history books written by both sides of the regime. Here I think 龍’s book is valuable in documenting many stories of the common people before they pass away or fade away from the history. When you finish reading this book, you inevitably will have this feeling that wars are hell, terrible, disastrous & better to avoid them at all cost.

PS: 龍 應 台 is a woman. Her ‘野火集’ had a lot of influences to the society in Taiwan. If we rate the most influential women from Taiwan in the pass 60 years, we may come up with the list like this: (note: we are talking about INFLUENTIAL only, not GREAT, not PRETTY, not INTELLIGENT, not ...)

王錦雲 (釋證嚴) (Most influential in the time span: 1966-2010). Religion & Philanthropy
瓊 瑤 (1960-1980) Novel
鄧 麗 君 (1970-1990) Music
龍 應 台 (1990-2010) History & current affairs

Of course, this is subjective. I think everyone should have his/her list.

現 代 桃 花 源 & Choice of Life Style

If you have a chance to visit Philadelphia and Gettysburg, you will follow state highway 340 & go west. Don’t miss one little town called Intercourse. It is an Amish town. In case you haven’t heard of Amish people, Amish is a branch of Anabaptist. Because of their religious belief, they don’t serve in government & arm forces. They were persecuted & kicked out from Europe. They came to America & settled in Pennsylvania & eventually spread among mid-west states. I passed Intercourse twenty-five years ago. I visited the town for the whole day & very impressed what I have seen. It is a unique community and it is so much difference from the outside world. You wonder why & how it can exist in a modern society & keep its life style. Amish people don’t use AC electricity, radio, telephone, car, no bicycle either. But kids use scooter (toy type). They use horse & buggy for transportation. It is almost but not a complete independent society. For example, it depends on outside hospital for emergency & it has to buy gasoline from outside for its tractors. They can use gasoline but not ac electricity. Ironically, dc battery is ok. I can understand their logic. If they allow ac electricity in their house, the authority can’t control the use of radio, TV & a lot of communication gadgets. But if battery is ok, sure they can use transistor radio. In fact, if battery is ok, you can hook up a dc-ac converter to get 120v ac. There are a lot of contradictory & idiosyncrasies in this kind of society. It is like the society in China. The coexistence of communism & capitalism creates a lot of jokes. In fact, there is some similarity between these two societies. It boils down to the choice of life style. In both cases, they are state imposed. We, in this modern time, do select our life style individually (not by state). For example, some people choose not to use FaceBook, iPhone, cellular phone, tv etc. Some choose not to eat meat, beef, pork etc. This leads to the next question: Is religion also a choice of life style?

The Amish society can not survive without the protection of the modern government. The reason they got kicked out from Europe is that they couldn’t defend themselves. They don’t fight for other people & don’t fight for themselves either. We heard a lot of jokes about Quakers & some people resent the double standard they use. For example, in autobiography of Ben Franklin, he described a group of Quakers was on board of a war ship. When the ship encountered a British ship, they all got scared & moved to the lower deck. After the fighting was over, they came out and criticized the whole thing should be resolved in a peaceful manner without firing cannons. The religious belief can be so strong that you forget the obvious logic. Another example is that Jewish people don’t fight on certain days of the year. So the Roman picked the day & conquered them. This might be the reason why Jewish people don’t have their own country for so long. I doubt they still follow that good old habit. Otherwise the Moslem can easily wipe them out.

The western Europeans seem very open & tolerant these days. Perhaps Amish people can move back to where they came from. But they are content here in the US. If you wander around in Pennsylvania next time & somehow you enter some place looks like a 現 代 桃 花 源, it must be an Amish town. Don’t panic, you just look around & enjoy yourself. I guarantee you will get out safely & will not get lost next time either.

Law of Nature (自然律)

When we study the science, we encounter all kinds of Law. Sometime they surface with terms like Hypothesis, Postulate, Theory, Principle, Rule etc. In math we learn Axiom, Theorem, Lemma, Corollary and many others. In general, the definition of the terms is more rigorous in math. But in our daily life, the definition of Law has been abused often especially in the last 40 years. Have you heard about Murphy’s Law, Moore’s Law & Pareto’s Principle? Or Peter Principle, Parkinson’s Law, Count to Three Principle? If we examine these laws or principles closely, we find that they are far from laws. They are qualified at best as Adages, Rule or Guidelines. They can’t be proved rigorously & you can always find exceptions to the laws. They can’t even be qualified as hypotheses or postulates. They are just Rule of Thumbs. Let’s examine some of them. But before we dig in, let’s examine the definition of the terms & do some translations.

Theory: the principle on which a particular subject is based, 學說 (理論)
Theorem: a rule, especially in mathematics, that can be proved to be true, 定理
Corollary: an idea, or fact that results directly from a theory, 結論 (必然的結果)
Lemma: a proven statement used as a stepping-stone toward the proof of another statement, 引理 (輔助定理)
Law: a scientific rule that somebody has stated to explain a natural process, 定律
Principle: a law or a theory that something is based on, 原理 (法則,原則)
Hypothesis: an idea or explanation of something that is based on a few known facts but that has not yet been proved to be true or correct, 假說
Postulate: a statement that is accepted as true, that forms the basis of a theory, 假定 (假設)
Rule: a statement of what is possible according to a particular system, 規則
Rule of Thumb: 經驗法則
Guideline: rules or instructions that are given on how to do something, especially something difficult, 準則 (指導方針)
Adage: a well-known phrase expressing a general truth about people or the world, 格言 (諺語)

Murphy’s Law
"Anything that can go wrong will go wrong." Is this really true? No is the answer. It is almost true that given enough time & enough tries, it will happen. It is like saying, “I buy lotto & I will hit it eventually” or “I walk outside very often & eventually I will be killed by a thunder." So Murphy is not a law, it is just a Rule or Adage.

Moore’s Law
"The number of transistors that can be placed inexpensively on an integrated circuit has doubled approximately every two years." This one has been modified to 18 months instead of 2 years. Actually, the original one was one year, not two years. Now we know how accurate this one predicts. It is not a law, it can best be qualified as empirical formula.

Parkinson's law
"Work will always take as long as the time available for it." This one tries to explain or describes some human behavior. In many cases, it is true. But alas, it is not always true. Some difficult task can not be finished if there is not enough time allocated. This one can be used as a guideline for any project. This is especially true for annual tax return. Why? There are so many procrastinators that try to meet the deadline. You give them the deadline, so they just try to meet it. But it is also true that thousands of people sent their return well before 4/15 every year. Why? They just try to get the refund as soon as possible.

Pareto’s Principle
"The Pareto principle also known as the 80-20 rule, roughly 80% of the effects come from 20% of the causes." It is equivalent to state, 20% of the effects come from 80% of the causes. Here the cause & effect are independent, they don’t need to add up to 100%. For example, 15% of people pay 90% of the tax in California. The interesting part of this so-called principle is the number 80 & 20, why not 30 & 70? Anyway, this is another way to explain some human behavior. You can hardly find any natural phenomena fit in this scheme. This one is best qualified as a rule applied to the area of human activities, but it is far from a Principle. The corollary of this rule is that 64 % of the effects come from 4% of the causes. Is it true or is it a fantasy?

Peter Principle
"In a hierarchy, members are promoted so long as they work competently." Sooner or later they are promoted to a position at which they are no longer competent, and there they remain, being unable to earn further promotions. The corollary: "In time, every post tends to be occupied by an employee who is incompetent to carry out his duties" or "Work is accomplished by those employees who are not competent." No wonder our world is a mess since the world is functioned in an incompetent way. This is another rule to explain the structure of our society or our economic system. Is it a principle? I don't think so. At best it is qualified as a low end of Principle. But it is not in the same league as Uncertainly Principle.

Most of these laws are from the management circle of business world. They are not thinking rigorously, rather very loosely. Like “Invisible hand (冥冥中有一隻不可目見之手)” & "Greed, for lack of a better word, is good", they lead to the chaos in the world of finance, economy, wall street & business world. It destroys so many lives & creates some monster banks too big to fail. The taxpayers end up holding the bag.

PS0: Count-to-Three Principle: If you don't know at least three ways to abuse a tool, you don't know how to use it.

PS1: 說, 論 & 經: 這三個字,堂而皇之. But they have been abused badly too. We have many examples (some of them are not qualified as called):
粒子說,波動說,波粒說,原子說,孔子說,聽說,細說,好說,胡說,佛說,併吞說,媽媽說,總統說,道聽途說
群論,民約論,人口論,國富論,资本論,重商論,相對論,量子論,君王論,進化論,演化論,唯心論,唯物論,海杈論,不服從論,边際效用論,天体運行論, 血液循環論
人論,典論,違心論,股市崩盤論,小金投資論,大乘起信論,命理預言論,興趣無用論,正統無視論,高談闊論
佛經,聖經,拜撲經,可蘭經,道德經,詩經,樂經,易經,水經,山海經,三字經,媽媽經,罗織經,月經,日經,神經

春神

春天是欣欣向榮的季節,大家都歌頌它的來临. 記得我們小學常唱的一首歌,”春神來了”. 多年以後,我們仍記得這個曲子. 其歌詞清新可喜,又富進取情調. 歌詞如下:

春神來了怎知道？
梅花黃鶯報告。
梅花開頭先含笑，
黃鶯接著唱新調，
歡迎春神試身手，
快把世界來改造。

多年来,一直以為是中國的曲子. 後來長大慢慢才知道這是一首德國名謠. 雖然原歌詞主要以歌頌鳥為主,但仍然充 滿春天的氣息. 原歌詞如下:

Alle Vögel sind schon da,
alle Vögel, alle!
Welch ein Singen, Musiziern,
Pfeifen, Zwitschern, Tireliern!
Frühling will nun einmarschiern,
kommt mit Sang und Schalle.

Wie sie alle lustig sind,
flink und froh sich regen!
Amsel, Drossel, Fink und Star
und die ganze Vogelschar
wünschen dir ein frohes Jahr,
lauter Heil und Segen.

Was sie uns verkünden nun,
nehmen wir zu Herzen:
Wir auch wollen lustig sein,
lustig wie die Vögelein,
hier und dort, feldaus, feldein,
singen, springen, scherzen.

其英譯文如下:

All the birds are already here,
All the birds, all!
What singing, music playing,
Whistling, chirping, trills!
Spring wants to arrive now,
It comes with song and sounds.

How cheerful they all are,
They move, nimble and gay!
Blackbird, thrush, chaffinch and starling,
And a whole cloud of birds
Wish you a happy new year,
Higher holiness and blessing.

What they announce to us now
Go straight to our hearts:
We want to be cheerful too,
Cheerful like the little birds,
Here and there, out and in the fields,
We want to sing, to jump, to joke.

You can listen to the song in the following youtube link:
http://www.youtube.com/watch?v=vHC-Io6q3zg

Top 10 Classical Music

In good old days, you always found some radio stations played classical music all day long. Some of them had special programs at specific time of the day. Also you found a lot of cities had their symphony orchestras. When time goes by, the number of them dwindled & a lot them simply disappeared in the thin air. It seems the market of the classical music get smaller each year. Does this mean the interest of people change? Yes & no, here are some of my observations:
1. There is not much innovation in the format of concert. People get bored when nothing is new or exciting. This is especially true for the young generation. I think the conductor should say something about the uniqueness of the concert instead of saying nothing & play.
2. The package of the classical music is not good enough to attract young people. For example, when people see Un Bel Di on CD, they don’t have any clue if there is no explanation on the cover. This is true for most of the arias of opera.
3. Radio stations lack of creative programs & enthusiasm.
4. CD is not cheap enough. Especially you have to buy the whole disc, not just one piece of music.
5. Only things bucking the trend are Three Tenors, Andre Rieu, Vienna New Year Special Program, PBS special music program, competitions, auditions etc. They are all something new in the musical package.
6. Internet & electronics suddenly change the market. Now you can buy a single piece of music at $1 & load it to iPod or something similar.
7. Only high profile orchestras survive. They record series music for Grammy awards or others.

Radio station KDFC is the only survived station that broadcasts 24 hours classical music in San Francisco. It gets the poll from the audiences for Top 100 Classical Music. It also creates a package this year that loads all 100 pieces of music in iPod & sells it at $299. If this is not revolutionary, it must be a quantum leap in music distribution. If you try to buy CDs to complete this top 100, you will have to spend more than one thousand dollars.

Here is the list of KDFC’s Top 10 of 2010 (the parenthesis is the rank of 2009)
1. Beethoven Symphony #9 (1)
2. Rachmaninoff Piano Concerto #2 (10)
3. Vivaldi Four Seasons (2)
4. Dvorak Symphony #9 (7)
5. Bach Brandenburg Concerto 1-6 (3)
6. Beethoven Symphony #6 (4)
7. Pachelbel Canon in D (11)
8. Gershwin Rhapsody in Blue (5)
9. Beethoven Symphony #5 (8)
10. Tchaikovsky Piano Concerto #1 (20)

This represents the taste & interest of the people in San Francisco bay area. In the past several years, the # listed in the top 10 change often. The only one consistent is the #1, Beethoven Symphony #9, Choral Symphony. It really shows the #9 of Beethoven is one & only one in its own class in most people’s mind. It is also the longest piece that takes almost one hour to play it from the beginning to the end. From #2 to #10, their ranks change every year. It says the taste of people changes every year. For example, Rachmaninoff’s piano concerto #2 jumps from 10 last year to 2 this year, a quantum jump. My list is different from the KDFC’s. I don’t mean my taste is better. It just means my taste is different from a lot of people. Here is my top 10 list:

0. Beethoven Symphony #9 (Choral)
1. Dvorak Symphony #9 (From the New World)
2. Beethoven Symphony #5 (命運)
3. Beethoven Piano Concerto #5 (Emperor)
4. Brahms Violin Concerto
5. Rachmaninov Piano Concerto #2
6. Beethoven Symphony #6 (Pastoral)
7. Schubert Symphony #8 (Unfinished)
8. Tchaikovsky Piano Concerto #1
9. Mozart Symphony #41 (Jupiter)

I do like to make some comments about KDFC’s list. Four Seasons & Canon in D are nice to the ear. But you just can’t listen to them often. Bach’s Brandenburg Concerto 1-6 is not uniform in quality. You just can’t lump them in one & try to compare to other classical music. It is more reasonable to pick #5 or #6. As to Rhapsody in Blue, it is just not exciting. Perhaps a lot people like jazz & pick this piece for the mood. I found that all pieces in my list are either symphony or concerto. I think it is fairly obvious as these two forms of music use extensively & intensively almost all instruments that we can find in an orchestra. The depth & power of expression & interpretation of human emotion are just too great to describe. Everyone should have his/her own top 10 list as everyone is different & special.

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.