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《心經》裡面的「般若波羅蜜」一詞

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很多年前曾經到過香港大嶼山的 心經簡林 。 心經簡林 是一個由三十八個巨型木簡，按數學無窮大「\(\infty\)」符號的形狀排成的木陣。在木陣裡面，除了第一個題目簡、第二十三個「空」簡和最後一個落款簡之外，其他的木簡都刻有《心經》的部分經文。 《心經》的全名叫《般若波羅蜜多心經》。我是在香港電影《 月光寶盒 》裡面，第一次聽到「般若波羅蜜多」這個詞的。在戲裡面，它是周星馳先生用來開啓可以讓時光倒流的月光寶盒的密語。必須注意的是，周先生把咒語唸成了「般若波羅蜜」，把「多」字給去掉了。 月光寶盒 的密語：般若波羅蜜. . . 不管「般若波羅蜜多」或是「般若波羅蜜」，念起來很別扭，很明顯它們都不是漢語，事實上，它們是由三個印度字組成的合成詞。「般若」的巴利語「paññā」的音譯：是知識或智慧的意思。「波羅」是巴利語「pāra」的音譯，它和英語前綴「para」一樣，是超越的意思，例如，英語「paranormal」就是超自然的意思。「蜜／蜜多」是巴利語「mī/mīta」的音譯，它是希臘語「metron」的親戚，也是英語「mete」或「measure」的祖先，想表達的是既定或肯定的意思。 把「paññā」+「pāra」+「mī」三個印度字連在一起，「般若波羅蜜」指的便是一種備受肯定、完美超凡的智慧。在周星馳先生的哲學世界裡面，也只有利用這種完美超凡的知識transcendental wisdom，才能將時空逆轉。 大嶼山的心經簡林與數學的無窮大「\(\infty\)」符號 可惜的是，我們暫時還沒有發現這種transcendental wisdom。可喜的是，數學家倒是發現了很多transcendental number（ 波羅蜜數 ）。波羅蜜數是一種很特別的數，因為你必須用無窮大「\(\infty\)」的概念才能將它正確地寫出來。例如，銀行用來算 複利息 的「\(e = 2.718\ldots\)」，就是一个波羅蜜數。 $$e = 2 + \frac{1}{1+\frac{1}{2+\frac{2}{3+\frac{3}{4+\frac{4}{5+\frac{5}{6+\frac{6}{7+\frac{7}{8+\frac{8}{9+\frac{9}{\ddots}}}}}}}}}} = 2.718\...
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The children of Yap Ah Loy sued their mum in court (1898 - 1904)

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1957/0118652W In the Court of the Senior Magistrate at Kuala Lumpur Civil Suit No. 138 of 1898. In the matter of the Estate of Yap Ah Loy, deceased, between Yap Hon Chin (28) Yap Loong Shin (23) Yap Leong Soon (18) Yap Kim Neo Yap Leong Sem by his next friend Ong Chi Siew Yap Leong Fong Plaintiffs and Kok Kang Keow (48), otherwise called Kok Ngeo Nga who is sued as Administratrix of the Estate and Effects of Yap Ah Loy, deceased. On the tombstone of Yap Ah Loy, we were given the following list: 1 隆興 (b. 29 December 1869, d. 5 January 1933), 2 隆盛 (Loong Shin, b. 4 April 1875, d. <1925?), 3 隆顺 (Leong Soon, b. 6 March 1880, d. 8 December 1907, died when he was only 27.8), 4 隆發 (b. 10 August 1882, d. 21 September 1900, died when he was only 18...
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The Mathematics of Honeycomb: Part II

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As explained in Part I of the article, instead of building their house with the easy method of hexagonal top + hexagonal bottom , honeybees are building their cells with hexagonal top + rhombic bottom . In this article, I will try to give a calculus-based demonstration on how the honeybees achieve the economization of their wax resources with a rhombic angle of 70°32'. Suppose we start with a hexagonal prism with flat bottom like the one shown in the figure above. Let \( AB = a\), \(A''A = b\). Then it can be shown that the surface area \(S_0\) and the volume \(V\) of this prism are: $$S_0= 6ab + \frac{3\sqrt{3}}{2}a^2, \quad V = \frac{3\sqrt{3}}{2}a^2b$$ respectively. Mark a point \(B'\) on the prism so that \(B'B'' = x\) and slice a tetrahedron from the prism along the line \(A''C''\) through point \(B'\). Then, flip and rearrange the sliced tetrahedron on top of the prism, as shown below. If you repeat this proc...
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Deification of Captain Shin

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. . . I pointed out how the Bandar, in refusing to accept terms and in fighting against his Sovereign, was a rebel, and that all who assisted him were rebels. That, as he knew well, two out of his three captains, China, had sided with the Bandar, and had given him (the Bandar) more than moral support in his recent operations. (I here showed him the Chinese document attached, which is an order of the head of the Macaos, Wong Hin, to any of his people to render prompt assistance at any time and in any way to the Bandar) . . . . after some more conversation we parted, but shortly afterward he brought to our quarters the two captains, China, I had been advising him about, Wong Hin and Ugoli Kim, and said that, as the Governor had sent me to assist him, he had made up his mind to put the management of everything into my hands . . . C. B. Plunket, Inspector-General of Police of the Straits Settlements November 30, 1874 Pa...
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Oratio Dominica: Malaica and Sinica

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In 1680, Andreas Müller (b. 1630, d. 1694) published a small book containing a collection of the Lord's Prayers in 83 languages. The work was later revised and expanded by other authors in 1700, 1705, and 1713. The following discussion examines the Malay and Chinese texts as presented in the revised edition published in 1713. The Lords Prayer in above a hundred languages, versions, and characters, published in 1713. Oratio Dominica ΠΟΛΥΓΛΩΤΤΟΣ ΠΟΛΥΜΟΡΦΟΣ. Nimirum Plus Centum Linguis, Versionibus, aut Characteribus Reddita & Expressa. Editio Novissima. Speciminibus variis quam priores comitatior. The work is built upon the earlier publication of Müller although the title page of the book did not explicitly mention any editor or author. In the Malay text, the Lord's kingdom 國 was rendered as ra'jat, using an old spelling system devised by Van Ophuijsen. It is...
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