Rigel Kent

Today is the first day of Ramadhan in Malaysia and about 30 days later, our Muslim friends will celebrate their New Year or Hari Raya Puasa. In Malaysia, the date of Hari Raya will normally be announced by the Keeper of the Rulers' Seal (Y. M. Engku Tan Sri Dato Sri Ibrahim bin Engku Ngah is the present Keeper) on Hari Raya Eve, who will read the following script in the TV. It is well known that the Islamic calendar is a lunar calendar and the sighting of new moon will determine the first day of the month. Not too long ago, I tried to tabulate the astronomical new moons (computed using a program by Legrand and Chevalley ), and the dates of Hari Raya Puasa celebrated in Malaysia, and the corresponding Chinese dates. The result is the following table. The following points can be inferenced from the table above: 1. If the astronomical new moon occurs ante meridian, then the Hari Raya Puasa will coincide with the second day in the corresponding Chinese month. 2. If the astro

《天南地北谈华语》是AIFM高级主播黄华敏制作的电台节目，两天前这个节目的主题是“ 司空见惯 ”这一句成语。这就碰巧跟我之前的一篇 贴文 的主题一样。 在这里我想针对黄华敏对“司空见惯”这一成语的出处和历史背景的理解做出一些点评。 节目里头说李绅请了一个漂亮的歌妓来给陪刘禹锡唱歌劝酒。这里用了“请”字，想必黄华敏是认为李绅是从外面请来了一名歌妓来娱宾。其实该名歌妓不是从外头请回来的，她是住在李绅的家里的家妓。所以李绅才能“以妓赠之”。 节目里头只给出了刘禹锡当时作的七言律诗的后面两句，并解释说这是刘禹锡作来送给主人家的。其实那一首诗的前面两句“鬟髯梳头宫样妆，春风一曲杜韦娘”是用来称赞该名妓女的美丽及歌艺。后面两句“司空见惯浑闲事，断尽江南刺史肠”是刘禹锡因为羡慕李绅家里有那么多的家妓的一时感触。就这样，刘禹锡只用了二十八的字就得到了他心仪的女人。 假设黄华敏见过《本事诗》的原文，那我只能整理出以下的结论： （一）她不了解唐人的性道德观。之前我说过，中国在唐代以前，对性和男女关系所持的态度是高度开放及不受礼教约束的。 （二）她不想讨论故事中“以妓赠之”的这一部分。但是如果不讨论的话，我认为我们没有办法真正的理解刘禹锡的“司空见惯浑闲事”到底指是什么。

司空見慣 是一句很普通的成語。 據《新華成語詞典》，這一成語出自唐代 孟棨 所編的《本事詩》。它通常用以形容某事常見，不足為奇。有鑒於《新華成語詞典》給出的典故不是很完整，我想在這裏補充一下。 在《本事詩》的 第一章 里頭，孟棨記錄了以下的文字： 劉尚書禹錫 826年冬天 罷和州 ，為主客郎中、集賢學士。李司空罷鎮在京，慕劉名，嘗邀至第中，厚設飲饌。酒酣，命妙妓歌以送之。劉於席上賦詩曰： 鬟髯梳頭宮樣妝，春風一曲杜韋娘。 司空見慣 渾閑事，斷盡江南刺史腸。 李因以妓贈之。 在唐代，一般有錢人都有自己的歌舞團和家妓，客人到訪時，主人家就會安排她們出來表演及陪酒。有一次詩人劉禹錫 (b. 772, d. 842) 到司空大人(大概相等於現在的工程部長) 李紳 (b. 772, d. 846) 的家里做客，對其中一名歌妓有好感，隨即便做了 斷盡江南刺史腸 這樣肉麻的詩句來泡妞。主人李紳一聽馬上知曉其意，因為仰慕劉禹錫的才華已久，便把該名歌妓送給了五十四岁的劉禹錫帶回家。 這個故事給出了唐代歌妓的定位：基本上她們只是主人娛樂客人的工具。只要客人喜歡，主人就可以將她們當禮物來送給客人，其中無需考慮歌妓自身的感受。 更重要的是，這個故事說明在唐代(和唐以前)，中國人的性觀念的很自由和高度開放的，所謂禮教基本上只是理論上的東西，沒有人會把禮教應用在男女關係和性方面。高流動的性關係乃屬司空見慣的事。唐以後，宋儒開始大力提倡禮教，才導致中國人性文化倒退和性觀念徹底改觀。

In Part I of the article, we considered the expression for computing the probability that at least r people will have the same birthday, given n people are selected at random. In this article, we will consider a special case to illustrate the use of formula numerically: Suppose five people are selected at random, what is the probability that at least three people will share the same birthday?" In this example, the Frobenius equation n 1 + n 2 = 5 has three sets of solutions and they can be tabulated as follows: Following McKinney, we define the general form of the probability P ( n ; n 1 , n 2 ) as It follows that P ( E ) can be computed as follows: The required probability that at least three people are sharing their birthdays is therefore: Alternatively, we could also arrive at the same result if the problem is approached from another direction, but we would require a slight modification on McKinney's formula. The required probability is thus the sum

In 1966, E. H. McKinney of Ball State University published a paper entitled "Generalized Birthday Problem" in the American Mathematical Monthly, in which he seek to answer two questions related to the famous birthday problem . The problems considered by McKinney are (a) Suppose n people are selected at random. What is the probability that at least r people will have the same birthday? (b) What is the smallest value of n such that the probability is greater or equal to 1/2 that a least r people to have the same birthday? What follows is the solution by McKinney with some notational adjustment. Let X j ( j  = 1, 2, ... , n ) be the n random birthdays, let event E ' be defined as " r or more birthdays are equal" and the event E be defined as "none of the r random birthdays are equal", then we obviously have P ( E )+ P ( E ') = 1, in which P ( E ) can be computed by summing the probabilities of all ways in which the n random birthdays ca

In the first two parts of the article, I have given a historical review of the honeycomb problem and a calculus-based technique to compute the honeycomb rhombic angle . In this article, I will try to give a crude analysis on the results we obtained in Part II . For a closed curve in two-dimensional space, there exists an inequality to govern its perimeter \(L\) and area \(A\): $$A \le \tfrac{1}{4\pi}L^2$$ This inequality is called the isoperimetric inequality . It simply means that the ratio of \(A/L^2\) cannot be greater than \(\frac{1}{4\pi}\). This result can be generalized to three-dimensional space to give: $$V \le \tfrac{1}{6\sqrt{\pi}}S^{3/2}$$ This shows that the theoretical maximum \(V/S^{3/2}\) (when you have the least surface for a given volume) is \(\frac{1}{6\sqrt{\pi}} = 0.0940\). For honeycomb cells, the ratio of \(V\) to \(S^{3/2}\) is: $$\frac{V_{\rm honeycomb}}{(S_{\rm honeycomb})^{3/2}} = \frac{\frac{3\sqrt{3}}{2}a^2 b}{\left(6ab + \frac{6}{\sqrt{8}}a^2

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

To understand how calendrical matters were handled by the Shang 商 Chinese. It is important to learn to count numbers in modulo 60 . The reason for their preference of modulo 60 is not exactly known, probably the ancestors of the Shang Chinese shared a similar set of extrasomatic knowledge with the ancestors of the Babylonians when they were still in North Africa . The current norm of handling the grouping of days is to use modulo 7: \(L\) Day count Name of the day 1 Day 1 Monday 2 Day 2 Tuesday 3 Day 3 Wednesday 4 Day 4 Thursday 5 Day 5 Friday 6 Day 6 Saturday 7 Day 7 Sunday The ancient Chinese, however, used several different styles to count their day of w

The fact that honeycombs is hexagonal is rather well-known. However, this is only a two-dimensional description of the honeycomb. The three-dimensional description of the honeycomb structure is more interesting, but most people are unaware of it. The base of a honeycomb unit cell is a composite surface formed by three rhombuses A real honeycomb has many cells. Each cell is a special type of hexagonal prism. The usual hexagonal prism has a flat hexagonal base, but the bottom of the honeycomb cell is not flat. The base of a honeycomb unit cell is a composite surface formed by three rhombuses . When many of these unit cells are glued together side-by-side, a slab is formed. And when two of these slabs are glued back-to-back, a honeycomb is formed. When the bases of many honeycomb unit cells are glued together The first person who took the trouble to measure the angle of the honeycomb structure is a French astronomer named Giacomo Filippo Maraldi . In 1712, Marald

The name  Gohonzon (ごほんぞん) is the romanization of the Japanese pronunciation of the Chinese word Yu Benzun (御本尊). The word Yu (御) is honorary prefix, while Benzun (本尊) means object of enshrinement in this context. For members of Soka Gakkai (創価学会) and Nichiren Shoshu (日蓮正宗), it may be considered as the object of veneration, at least when they are practicing Gongyo (勤行). From an artistic point of view, Gohonzon is technically a piece of calligraphy written in mixed Chinese regular script (楷书), semi-cursive scripts (行书) and Siddham scripts, they were first produced by Nichiren (日蓮, 1222-1282), a Japanese monk who lived in the Kamakura period (鎌倉時代). The first Gohonzon (called Yojihonzon , 楊枝本尊) was designed and inscribed by Nichiren in November 19, 1271 (文永8年10月9日), when he was 49 year-old. Between 1271 to 1282, Nichiren actually designed and produced more than 120 mandalas for his disciples, not all of them were identical. But the general trend is that the design of the Nichiren

\(\pi\) is a fundamental constant in mathematics. It is also an important constant in science for it appears naturally in so many applications: in the period of a simple pendulum in mechanics , Maxwell-Boltzmann distribution for gas molecules in thermodynamics, Coulomb's law for electrostatic force in electromagnetic theory, Heisenberg's uncertainty principle in quantum mechanics, Einstein's field equation in general relativity theory. Since \(\pi\) is such an important constant, it should be properly introduced to students, both historically and mathematically. In Malaysian secondary schools, this constant is first taught to a typical 14-year-old when he/she is learning the geometric properties of the circle. In a recent book titled "Essential Mathematics Form 2", published by Longman, the authors wrote, in page 163, the value of \(\pi\) is an estimated value, which is \(\frac{22}{7}\) or 3.142 This remark is technically incorrect. I guess the authors p

In most of the secondary school level mathematics reference books found in local bookstores, the mathematical object "circle" is introduced as follows: A circle is a set of points that are equidistant from a fixed point. There is something wrong with this description. It is rather vague because a set of points could mean the following set of 8 points {P1, P2, P3, P4, P5, P6, P7, P8}: Although these points are equidistant from a fixed point, this particular set does not form or look like a circle. This problematic description of "circle" is not entirely the fault of the reference book authors, because it actually originates from page 45 of the Curriculum Specifications for Form 2 Mathematics, compiled in 2002, by the Curriculum Development Centre, Ministry of Education Malaysia. I must say that it is rather difficult to describe "circle" or any other mathematical objects with words. A better version (but still imprecise) would be: A circle is a c

The nucleus of the story of Hikayat Hang Tuah was born during the Malaccan period in the 15th century, but its cytoplasm contains elements from Sejarah Melayu and the Johore Sultanate in mid 17th century. The final form of Hikayat Hang Tuah as we now know it was last edited probably in 1710s, 250 years away from the Malaccan period, 300 years away from now. Some web sources suggest that Hang Tuah was actually a Chinese, and recently a friend of mine raised the same question to me. I personally do not think Mr. Hang is a Chinese, although it is very inviting to think of "Hang" as a word of chinese origin, like what I postulated in the case of Hang Li Po . In fact, my family name was spelt as "Hang" instead of "Ang" during the time of my grandfather's father when he followed his boss Tan Kah Kee (陈嘉庚) to Nanyang. Now back to Hang Tuah, he is definitely a pseudo-character, probably loosely modelled after a real person - Laksamana Abdul Jamil . Abdu

The icon and slogan found on the paperbag of Eu Yan Sang (余仁生) chinese drug store: (咸因)有心才会感恩 (approximately: Be grateful (to your parents), if you have heart) reminds me of an hexagram in the Chinese divinational classic. For the uninitiated, the slogan is a clever manipulation of Xian Yin (咸因) and Gan En (感恩). In the former, the hearts (心) are removed, and does not carry any meaning in modern Chinese. My guess is that the creator of the slogan did not know that the character Xian (咸) is actually a primitive form of the character Gan (感), a verb meaning sense or feel. Now back to the hexagram business, there are altogether 64 hexagrams documented in Yi Jing (易经, Wade-Giles romanization : I-Ching). One of them is very interesting from a human reproductive perspective because it contains the instructions on how to carry out foreplay before penile-vaginal penetration, it is Hexagram No. 31, known as Hexagram of Xian (咸卦). Given below is my translation of the interpretation

Some days ago, I chanced on a new book by Tunku Halim at MPH. The book title is "History of Malaysia: A Children's Encyclopedia" . As a check on the factual accuracy of the book, I turned to the Parameswara section to see what Tunku has to say about him. To my horror, I read: Parameswara was married to Hang Li Po. Tunku's statement is incorrect for the following reasons. 1. According to Sejarah Melayu, Hang Li Po was a Chinese princess married to Sultan Mansur Shah, not Parameswara. 2. Reputable historians in general doubt the historical existence of Hang Li Po, because the name of the princess cannot be found in the Chinese or Portuguese sources. It is only mentioned in Sejarah Melayu. And Sejarah Melayu is full of historical inaccuracies. Concerning the origin of the name of the Chinese princess, I offer the following explanation. The name "Hang" is easy, it is simply a transliteration of the word "汉", meaning Chinese, or the word could possibly

A friend of mine is mycophobic. She is afraid of seeing living mushrooms and couldn't handle them as cooking ingredients, but she can eat them when they are cooked. I am curious about the exact etiology of mycophobia, but it is not well-documented in the literature. I rarely find any scholarly discussion on mycophobia. Many suggests maybe mycophobia has a cultural basis. My guess is that mycophobia should not be memetic. It should have a genetic basis. It should be hardwired in the DNA program and is transferrable to the next generation. Although this function is no longer very useful in the modern world. In the long history of human evolution, some groups of human, possibly living in a region surrounded by many poisonous species of fungi, must have evolved the defense mechanism to avert fungi species, for the fear of consumption of deadly mushroom species. This DNA trait is important for the survival of that particular human groups. I offer two hypotheses on the mechanism of mycop

The official emblem of the state of Malacca shows two light brown mouse deers on each side of the tree of Malacca. This depiction is rather problematic. Because, if the emblem is meant to commemorate the brave Sang Kancil , as encountered by Parameswara in the Sejarah Melayu, then the color of the animal is probably not correct. If you follow the Malay classic carefully, the Sang Kancil mentioned is not light brown but white . The relatively new The logo was unveiled when Malacca was declared Historical City on April 13, 2003 logo of the City Council of Malacca, however, correctly show the two mouse deers in white . On the other hand, the Sang Kancil story purported to explain the founding of Malacca could be a story modified from a folk-tale from Sri Lanka. This fact was first noted by R. O. Winstedt (1922) Two Legends of Malacca, Journal of Straits Branch of Royal Asiatic Society, Vol. 85, p. 40. I was in the Za'ba Memorial Library , around

In Chinese fate calculation, there exists a mapping between the wuxing (五行) and sexagenary components (celestial stem, γ = tiangan 天干 and terrestrial branches, ζ = dizhi 地支). When the birthdate of a person is stated in sexagesimal form, one is able to deduce the xing associated with the eight sexagenary components or bazi (八字). Normally this mapping is in table form: A useful set of numerical formulas to handle the mapping is to use The basic principle to compute the mutual compatibility of two sets of sexagenary birth data is to pair the corresponding sexagenary components of the two individuals and compute their compatibility coefficients. We can then construct a normalized rank based on the eight compatibility coefficients computed, and "foretell" whether the two individuals can live in harmony.

今天早上八点一条Allianz的保险代理跑来跟我讲关于他们公司的风险分析(risk analysis)和医疗核保(medical underwriting)的程序。有时候一些医疗报告及医疗概率常会被错误诠释，这对受保人是有欠公平的。 这里要讲一则几年前英国发生的事件，在这个案例里，数学概率被一位著名的医学博士错误应用及解读，造成一名母亲含冤入狱。 1999年11月，35岁的英国妈妈莎丽克拉克(Sally Clark)被指分别在1996年11月29日和1998年1月26日谋杀她两个只有几个月的男婴。这两名男婴去世时分别只有82和58天大。 案子的“专家证人”是一个叫罗伊梅都(Roy Meadow)的小儿科教授，来自英国利兹大学(University of Leeds)。罗伊教授认为这个案子不属于婴儿突然死亡候群症，因为两个连续婴儿猝死的或然率是1/8543 x 1/8543 = 1/72982849，也就是一对7千3百万。 如果这个概率的计算是对的，那么两名男婴被谋杀的相对概率是99.9999985巴仙。 结果，数学白痴的陪审团以10对2票认同莎丽谋杀，法官判莎丽终身监禁。 关于罗伊教授概率算法，英国皇家统计学会(Royal Statistical Society)曾在2001年发表过一份声明，表示罗伊教授的此项推导是没有统计学根据的。英国皇家统计学会主席更亲自写了一封信给英国大法官表示对此事的遗憾。 一名叫玛丽莲的律师觉得事有蹊跷，她挖出了一份之前没曝光的病理化验报告。报告里表明莎丽的二儿子是感染了金黄色葡萄球菌(Staphylococcus aureus)，应属自然死亡。 2003年，莎丽第二次上诉得直获释，但是可怜的莎丽已经白白做了3年的牢。 2005年，罗伊教授被英国医学总会开除会籍。罗伊教授上诉，一年后又恢复了他的会籍。 这几年的经历给莎丽带来巨大心理压力，她始终无法从新振作。2007年3月，莎丽因为酒精中毒死亡。