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Long division of infinite series

Long division of numbers is usually taught in primary schools to children as one of the basic arithmetic skills. Consider, for example, \(486 \div 5\).

It technically requires the child to atomize 486 into blocks of fives. There is a number of ways to split the number. Since we know that \(90 \times 5 = 450\), one way to do \(486 \div 5\) is: $$\begin{align}486 &= (\mathbf{90} \times 5) + (480 - \mathbf{90} \times 5) + 6\\ &= (90 \times 5) + 30 + 6\\ &= (90 \times 5) + (6 \times 5) + (5 + 1)\\ &= (90 + 6 + 1)\times 5 + 1\\ &= 97 \times 5 + 1 \end{align}$$ We can also repeat the process with a different seed number, for instance, instead of 90, we can start with 80: $$\begin{align}486 &= (\mathbf{80} \times 5) + (480 - \mathbf{80} \times 5) + 6\\ &= (80 \times 5) + 80 + 6\\ &= (80 \times 5) + (50 + 30) + (5 + 1)\\ &= (80 + 10 + 6 + 1)\times 5 + 1\\ &= 97 \times 5 + 1 \end{align}$$ This essentially means that 486 can be atomized into 97 blocks …

The Bahasa Malaysia July Paper of 1976

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In 1960, Bahasa Melayu was gradually dosed into our national schools as the language of instruction. But it wasn't until 1970 that the Bahasa Melayu paper in MCE (Malaysia Certificate of Education) was renamed to Bahasa Malaysia and was made a compulsory subject. It means that you need to pass your Bahasa Malaysia in order to pass your MCE.

And in order to get into Form Six, which was then the only way for a middle class student to get a university education, a pass was not good enough, at least a weak credit is needed to secure a seat in HSC (Higher School Certificate). The introduction of the Bahasa Malaysia July Paper was essential because a lot of good students failed to obtain a pass or a credit when they sat for their Bahasa Malaysia paper for the first time.

The MCE 1972 result, as announced by the then Education Minister, Inche Hussain Onn, on Wednesday, 4 April 1973
GroupPassedFailed BahasaGeneral failureTotalMalays6,7511462,4459,342Non-Malays9,31414,1164,35427,784All1…

Mahavira and Nobi Nobita

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The opening title of the 1988 film Nobita no Parareru Saiyūki 大雄平行西遊記. This film is perhaps the only film where you can find Mahavira 大雄 and Nobita 大雄 together The main hall of a Mahayana buddhist temple is normally known as the Mahavira Hall or 大雄寶殿 (Dàxióng Bǎodiàn) in Chinese.

The following calligraphic plaque, for instance, was photographed two years ago when I was at Kaiyuan Temple 開元寺 in Quanzhou 泉州.
Mahavira Hall of Kaiyuan Temple, Quanzhou The four chinese ideograms symbolising both Mahavira and the hall are rendered by a certain magistrate of Quanzhou named Sun Chaorang 孫朝讓 in standard script 楷書, probably on the 15th day of the 8th month of the year of Renwu of Chongzhen 崇禎壬午仲秋 (Proleptic Gregorian: August 29, 1642).

If you pay attention to the two vertical lines on the plaque, you will notice that the regnal name of Emperor Zhu Youjian, 崇禎, and the name of the calligrapher were both written in red ink.

Apparently writing your name with a red pen was not actually a probl…

吉隆坡塔動物園一隻叫nabeh的動物

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罵髒話和一個人的文化水平沒有直接的關係。

罵髒話不代表妳文化水準低。相反的,不罵髒話也不代表妳文化水準高。比方說,我跟車間的同學去喝酒,同學問我要不要唱歌,我接連搖了幾次頭。同學便開玩笑地說:你的小鳥應該會唱歌唄?

同學所指的鳥並不是動物學的,她所指的鳥其實是

鳥(niǎo)是屌(diǎo)通過聲母撤換之後得來的,轉音之後,鳥的不雅指數似乎有所降低。

中國有許多文人有時也跟同學一樣喜歡用鳥來稱呼人。著名學者胡適先生就曾經用鳥來形容北洋政府。 大家合起來,趕掉這群狼,推翻這鳥政府,起一個新革命,造一個好政府,那才是好政府的紀念了!
首見於1921年10月,為紀念辛亥十週年而發表的《雙十節的鬼歌》。《胡適文集》卷九,第178頁 幾年後我們看見魯迅先生在文章裡面也用鳥來稱呼人。 問什麼荊棘塞途的老路,尋什麼烏煙瘴氣的鳥導師!
首見於1925年5月,魯迅在《莽原》週刊一篇叫《導師》的文章。《魯迅全集》卷三,第56頁Blue Bird的手作羊毛氈—兩隻可愛的羊駝娃娃 鳥語一番後讓我接著說馬,我要說的其實是一種不馬不羊不駝、一種叫草泥馬的動物。這種動物,你可以在吉隆坡塔旁邊的小動物園找到。草泥馬其實是髒話「肏妳媽」的淨化版,據說它是十年前中國網友的發明。
吉隆坡塔動物園靠近出口的地方養了一只叫草泥馬的羊駝,我在出園前給它的四隻腳趾頭照了一張特寫。 因為馬的閩南發音是bé/beh,所以我們也可以把羊駝叫成nabeh。Nabeh和草泥馬一樣,是「我肏你媽」的淨化版。不同的是,nabeh省略的是主詞「我」、動詞「肏」還有「媽」的「女」字旁。

跟nabeh同源的髒話還有niamah和walaueh等,我的許多同學都喜歡把nabeh,niamah和walaueh等字掛在嘴邊,習慣性將它們當語氣助詞來強化語句。當然nabeh,niamah和walaueh是在眾多髒話裡頭相對比較乾淨的幾個,所以聽入耳也不覺有太大的殺傷力。不過,我孩子的媽媽還是不喜歡她的兩個兒子開口閉口walaueh。

Nabeh,niamah,walaueh,草泥馬和其他比較乾淨的髒話 當我們用這些字的時候,其實是完全沒有肏你媽的意思在句子裡頭的。本地著名播音人Patrick Teoh的其中一個部落格就是用niamah來命名的,而他也喜歡用niamah來總結他寫的貼文。例如,幾天前為了表示…

媽媽為孩子搬兩次家的故事

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山東的單親媽媽和她的獨生子孟軻先生搬兩次家的故事,是出自《列女傳・母儀・鄒孟軻母》裡頭的一段文字。原文是這樣的: 鄒孟軻之母也,號孟母,其舍近墓。孟子之少也,嬉遊為墓間之事,踴躍築埋。孟母曰:此非吾所以居處子也。 乃去,舍市傍,其嬉戲為賈人衒賣之事。孟母又曰:此非吾所以居處子也。 復徙舍學宮之傍。其嬉遊乃設俎豆揖讓進退。孟母曰:真可以居吾子矣。遂居及。 從G點搬去M點,我們叫一遷。若再從M點搬去S點,也是一遷。從G到M再到S,總共搬了兩次家,理應稱為二遷。例如。舊時秦國從周朝最初的封地西犬丘到嬴政時代的咸陽城,總共換了九個首都,我們叫九都八遷。 M:媽媽不喜歡孟子以營銷(marketing)為主題玩遊戲 所以,孟媽媽從G點搬去M點再到S點的過程,應該叫「孟母二遷」而不是「三遷」。東漢文人趙岐先生(108年-201年)在給《孟子》一書寫的序的時候,第一次為孟媽媽搬家的次數做出錯誤的統計: . . . 孟子,幼,被慈母三遷之教。長,師孔子之孫子思,治儒術之道 . . . 出生於清朝乾隆年間的梁無非小姐(?年-1825年)在為《列女傳》做校注時,也是同樣支持趙岐在《孟子・題辭》所提的「三遷」。
G:媽媽不喜歡孟子以葬人(funeral)為主題玩遊戲 趙岐先生和梁無非小姐的「三遷」論,身為業餘天文學家的劉向肯定不敢苟同。劉向是《列女傳》的原創作者,是西漢的皇族,他的太公是漢高祖劉邦同父異母的弟弟。劉先生常常在家看星星看到天亮,他兒子劉歆受他的影響,後來也成為了數學家。劉歆可了不起了,他可是第一個不用圓三徑一的中國人。

《列女傳》裡面的105則故事,很多是劉先生瞎編的。他主要想是用漢朝大男人主義的角度,來約束女人和媽媽的行為。所以你讀《列女傳》的時候,需要小心一點。

劉先生在寫孟媽媽的故事時,用了兩次「此非吾所以居處子也」。第一次是孟媽媽看見孩子以葬人(funeral)為主題玩遊戲,第二次是孟媽媽看見孩子對營銷(marketing)有興趣。兩次都彰顯了孩子潛在的興趣,但兩次都被媽媽壓制。如果當時孟媽媽能給予適當的鼓勵,孟子長大成人或許能將「葬人」和「營銷」融會在一起,搞出一些像富貴山莊的生意。 S:孟子最後以俎和豆(ritual and ceremonial vessels)玩祭祀的家家酒遊戲,媽媽才沒意見 孟媽媽最後是看到孩子用俎和豆玩祭…

Concerning fuck

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In the English-speaking world, the word fuck is usually abhorred by many parents because it is a taboo-word to them.

The word is almost as old as the written language. The first recorded use of this monosyallable verb in the English literature can be found in the following 516-year-old lines, composed by the Scottish poet William Dunbar in 1503: His bony berd was kemd and croppit
Bot all with kaill it wes bedroppit
And he wes townich, fulich and gukkit
He clappit fast, he kist and chukkit
As with the glaikis he wer ourgane
Git be his feirris he wald haif fukkit
Ye brek my hairt, my bony ane!

H. Bellyse Baildon (1907) The poems of William Dunbar, with
introduction, notes and glossary, Cambridge University Press, p. 5. Fuck is perhaps one of the most flexible word in the English language, it can be used (a) as a verb or (b) as an imprecation (as the coarsest version of damn) or (c) as an adverb or (d) as an adjective, because of its expletive nature. For example, if I ignore …

Men and women see things differently

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Men and women see things differently. You do not have to be a married person to get my point, but if you are a married person, you can appreciate this fact more readily.

To explain this, I have to start from the beginning.

In the beginning, as we were told by the Abrahamists, God created the light. The light, as James Maxwell would like us to believe, is an electromagnetic wave.

To be able to see the world in colors, you need to use a special type of protein called opsin to convert the wave signal to electrochemical signal and feed it to the brain.
Behind the beautiful eye lays the mythical polychromatic opsin And in the beginning, God created a number of opsins, some of them are good at processing long wave (yellow and red), some of them are good at handling medium wave (green), and some of the them are only short wave sensitive (blue and ultraviolet).

After the creation exercise, the instruction for building the blue opsin block was carefully saved in Chromosome No. 7 (the p…