Thursday, March 30, 2006

Differential Equations and Eclipse

Differential Equations and Eclipse

They say the most beautiful equation for mankind is as follows:
e**(i *π) = -1

i = root(-1) = (-1)**(1/2): a unit imaginary number;
e = the natural (Napierian) logarithm, or 2.7182818…;
π (or pi) = the circular constant, or 3.14159265…
* * *

You may wonder what kinds of numbers are used in the most advanced mathematics and science. They use only four types of numbers: ordinary numbers (composed of basic numbers from 0 to 9), π, “e,” and “i.”

Even today, almost all the scientific and engineering documents can be read and understood, if you know the above four types of numbers.

The equation, e**(i *π) = -1, includes the all types of the numbers. Therefore, they say it is the most beautiful equation, or a miracle equation.

However, it is a direct result of Euler's formula:
e**(i * x) = cos(x) + i*sin(x), with x = π, and cos(π) = -1 and sin (π) = 0.

On the other hand, Euler's formula is a result of the following expansions:
cos (x) = Sum of [(-1)**k]*(x**2k) / [(2k)!] from k =0 to ∞;

sin (x) = Sum of [(-1)**k]*[x**(2k-1)] / [(2k-1)!] from k =0 to ∞; and

e**x = Sum of x**k / k! from k =0 to ∞

while k! = 1*2*3*…*(k-1)*k.

(Here if x = ix,

In this way, the imaginary number can be introduced in the equation.)

However, the key to the expansions is as follows:
d cos(x) / dx = -sin(x);

d sin(x) / dx = cos(x); and

d e**x /dx = e**x

while d/dx means differential by x.
* * *

The nature can be expressed and analyzed by differential equations. Thus what makes possible the most beautiful equation is definitions of the functions of e**x, cos (x), and sin (x) based on each differential equation.
* * *

It can apply to human beings. If a woman called a beauty ever exists, which Jesus Christ never assures us of, we can test her by differentiating her features. But, human differentiation might not be so simple as the above mathematical ones.
* * *

But, as for me, the equation, e**(i *π) = -1, does not seem to be the most beautiful equation. The key differentials do not look like so, either.

Right from the start, mathematics and numbers are tools, operations, processes, and methods. They can be nice or rational, but “beautiful” is too much.
* * *

If a woman loves God or Jesus Christ, her internal structure should be rearranged by love and faith so as to be able to respond to outer force, including men’s observation, in a well differentiated manner. Consequently, she should look beautiful in safety and security.

Otherwise, women should put on a veil. (Today, an eclipse happened on some part of the earth, mostly Islamic regions, symbolizing something.)


Tuesday, March 28, 2006

Hidden Code Discovered by a Bestselling Author: 1, 81, 1458, and 1729

Hidden Code Discovered by a Bestselling Author: 1, 81, 1458, and 1729

Even today, The Da Vinci Code, by Dan Brown, is one of the New York Times best-sellers. Its Japanese version is still one of the bestselling fictions in Japan, too.

(I am not so interested in Leonardo da Vinci and his works. He is a little too pagan to deal with a kind of spiritual thing, in my opinion.)

As for nonfictions, Night, by Elie Wiesel, is one of the best-sellers in the United States. It is interesting that a Holocaust-related book written by the 1986 Nobel Prize winner is still welcomed by U.S. readers. Someday, an Arab or a Muslim may write a best-seller concerning Iraq and the wars involving the country.

In Japan, one of best-selling nonfictions today is “Kokka no Hinkaku (Dignity of Country)” written by a popular mathematician.
* * *

The mathematician Masahiko Fujiwara is an interesting person. He has many American and European friends through his profession, which seems to lead him to deeply thinking about Japan and the world, in addition to influence of his late father, a famous novelist in Japan.

He once presented a special number which is equal to a sum of each number on each digit multiplied by a number made by reallocating each number of each digit of the sum reversely to its each digit, as follows:

1729 --> 1+7+2+9=19
19 ----> 91
19×91 = 1729

There are only four numbers in the universe that satisfy this operation: 1, 81, 1458, and 1729.

Mr. Masahiko Fujiwara is said to call this discovery the Ugly Theory. However, I don’t find any ugliness in it.
* * *

Mr. Fujiwara is strongly against two issues: globalization and compulsory English learning in Japanese elementary schools.

The reason is that the issues are based on simple logic which is dangerous.

People think if A is B, and B is C, while A is correct, then C is correct 100 percent. But, in reality, A and B can be only 10 percent correct. Then C is just one percent correct, since 0.1×0.1 = 0.01.

A and B can be anything, but people take “globalization” as C. Accordingly, they say that globalization is 100 percent correct.

Also, A and B can be anything, but people take “trendy English learning in Japanese elementary schools” as C.

Though their nominal aims are economic satisfaction of majority of mankind and fostering international-minded Japanese in volume, their logic is really ugly.
* * *

An example of a logic sly multinational businesses resort to is as follows:
A: Maximization of profits by expanding shares of business, which meets their real intention 100%.

B: Free invasion of untapped and undeveloped markets and economies, which assures maximization of their own profits 100% probably.

C: Selling in rosy globalization, which makes countries fully open up their market, resulting in achieving their true goal almost 100%.

Instead of using the above bare factors A, B, and C, they technically advertise to the world the following:
A: Economic satisfaction of majority of mankind (possibility 1%)

B: Promotion of local market through free trade and free entry based on wise selection by local consumers (possibility 1%)

C: Globalization as the most efficient means for achieving common prosperity (thus resultant possibility is 0.01%).

This is more sinful than ugliness.
* * *

In 1729, Ekaterina II Alekseevna, not “Miss EU” but the eighth Czar of Romanov Dynasty of Russia, was born in a former territory of Germany.

In 1458, the Queen's College of St Margaret and St Bernard was rebuilt in Cambridge, England. The College has a bridge called the “Mathematical Bridge” which people thought to have been built without nails (but it was found in the 20th century that the bridge had full of nails and screws).

In 81 AD, Arch of Titus was built in Rome to commemorate the victory of the emperors Vespasian and Titus in the war against Jews. Since then, it almost took a full span of ages for Jews to return to “Jerusalem.”

In 1 AD, "Japan" then called "Wa" was split into 100 countries, some of which sent official missionary to authorities, stationed in Korean Peninsula, of Han Dynasty of China. It is recorded in an official history book of ancient China.
* * *

There is one word that Jesus Christ has never used: ugliness.

Nonetheless, exceptionally Japanese might be allowed to say: if there are any dubious factors that might make ugly a logic, a story, history, or education, you should be on guard.


Sunday, March 26, 2006

Fateful 2001 in New York; Fateful 1932 in Tokyo

Fateful 2001 in New York; Fateful 1932 in Tokyo

A successful cartoonist in Malaysia said that you should not take anybody as a subject into your work if you bear ill toward him or her.

It must be a key to success a humble artist has learnt in a multi-race and multi-religion environment in Southeast Asia, which should apply to all cases.
* * *

On September 11, 2001, a Japanese was watching the World Trade Center towers burning and crumbling down to the ground zero from her residence in New York.

Mrs. Sadako Ogata, United Nations High Commissioner for Refugees (UNHCR) from 1991 until 2001, was at that time working on her memoir in New York.

The great-grandchild of a famous Japanese prime minister was then in New York after having terminated her mission in Afghanistan Japan and UNHCR had been pursuing around 2000.

In Washington D.C. two months later after the 9/11 Attacks, Mrs. Sadako Ogata was making a speech in a high-level talk with Mr. Collin Powel and Mr. Paul Henry O'Neill, two key Secretaries of the then U.S. Government, on her experiences in Afghanistan.

She continued to play a major role, such as Special Representative of the Prime Minister of Japan at the International Conference on Afghanistan.
* * *

She was working on Afghanistan in 2000. She flew to Pakistan and Afghanistan to meet with Taliban leasers and also inspect situations concerning girls’ education under the Taliban regime.

However, according to her reports, all the foreign countries, except Japan, had lost interest in Afghanistan and left the nation. Eventually, she left the project and returned to Japan. Everything about Afghanistan seemed to be terminated. Then she moved to New York and started to write her memoir.

Fatefully one day in New York in 2001, she eye-witnessed the World Trade Center buildings burning and falling down, without knowing the attackers on board the jet planes were put at the helm by their headquarters in Afghanistan.  
* * *

In fiscal 2000, Japan contributed a half million dollars through UNCHR to aid for Afghan refugees, as well as 1.1 million dollars to support for Pakistan and another 1.1 million dollars to Iran in connection with aid for refugees therein. Through U.N. World Food Program, Japan also provided foods worth 5 million dollars for Afghanistan in FY 2000. In addition, Japan provided medical support worth 240,000 dollars for Afghanistan and Pakistan through International Committee of the Red Cross in FY 2000.

(After the 9/11 Attacks, Japan has contributed about 600 million dollars to various Afghanistan-related projects.)
* * *

A Japanese reader of Mrs. Sdako Ogata’s book wondered why the female scholar, a daughter of a diplomat, decided to work on the ground in troubled regions in the world when she got 60 years old. (Her relatives include many famous upper-class families in Japan.)

Mrs. Sdako Ogata’s great-grandfather became prime minister of Japan in 1931; however, in the next year 1932, he was assassinated by a terror group including young officers of the Imperial Japan’s Military.

It is also interesting to know that her great-grandfather, Tsuyoshi Inugai, had once personally helped Sun Yat-Sen (also know as Sūn Wén), Father of Modern China who led people in the chaotic terms after the collapse of Qing Dynasty.
* * *

God seems to have prepared, for Japan’s difficult moment in the outset of the 21st century, the daughter of a daughter of a daughter of the prime minister who had become a symbol of democracy and victim of terror in Imperial Japan before Word War II.

(Mrs. Sadako Ogata reportedly refused Prime Minister Junichiro Koizumi’s offer for the position of Foreign Minister in 2002 when then Foreign Minister Makiko Tanaka, a daughter of another prime minister who had met Mao Tse-Tung in Beijing in 1972, was dismissed. It might indicate another key to success for fateful people.)