Hindu-Arabic notation is strictly positional. It means if we stick an Arabic ‘٤' (4) to the left of an Arabic ‘١' (1), we would normally get a ‘٤١' (41).
$$4\times 10 + 1 = 41$$
If for one moment, suppose the glyph for ‘5' is yet to be invented and we are asked to supply one.
Excuse me, how do you write ‘five'?
One easy way is to copy the Romans: We pretend the rule is not positional but additive, i.e.
$$٤+١=4 + 1 = 5$$
However, for our new design to function properly (and to prevent mix-up) in the positional scheme, they must be fused tightly together into one single glyph. And the result is something that looks like a mirror image of B (B) or a Gujarati ‘ઇ' (i).
٤
١
Now, this gedankenexperiment can be repeated if you start with ઇ (5) and remove the vertical stroke (1) on the right to get 4 (٤). Given the fact in most early mathematical manuscripts, four is consistently written as ۴, it is more likely that ٤ is manufactured from ઇ by Mashriki scribes. The reason why ۴ is kept in Persian/Sindhu keyboard but abandoned in Mashirki keyboard is not exactly known.
۱۲۳۴
B in old mathematical tables
The Persian engineer Abū BakarMuḥammad ibn al-Ḥasanal-Karaji (953 - 1029) must have produced the first written record of binomial coefficients (arranged in the form of Pascal's triangle) but his work is lost.
See Mustapha Nadmi (2019) A Significant step toward the development of algebra: Al-Samaw'al Ibn Yahya Al-Maghribi, a twelfth century mathematician, PhD Thesis, Columbia University.Binomial coefficients in MSS Ayasofia No. 2718, 116ff, the oldest extant copy of al-Bahir fi al-Jabr (in Suleymaniye Library in Instabul, Turkey). The manuscript was discovered by Max Krause in 1936 in Istanbul. It was copied on 24 April 1325, about 150 years after the death of its author. Another slightly younger copy is available and it is Esat Efendi No. 3155.
Fortunately when al-Samaw'al ibn Yahyaal-Maghribi (1130 - 1180), a muslim Jewish mathematician, wrote his al-Bahir fi al-Jabr (The Brilliance in Algebra), he cited al-Karaji's al-Fakhri fi al-Jabr wa al-Muqabala (The Brilliance in Algebra and Equation Balancing) as one of his reference. In al-Maghribi's table of binomial coefficients \(n \choose k\), we can see first two ‘5's when the case for \(n = 5\) is written down, that is, \(5 \choose 1\) and \(5 \choose 4\). In both cases, the number is rendered as B.
B
The B-glyph is repeated throughout the table with the vertical line closing the loop. Occasionally, however, the loop is not 100% closed, as in the case of \({10 \choose 2} = 45\), and \({11 \choose 2} = 55\).
al-Maghribi's table of powers, \(2^p\) and \(3^p\). The mirrored-B five is shown in \(2^8 = 256\), \(2^9 = 512\), and \(3^8 = 6561\).
Kitab al-Amal bi al-Asturlab of al-Khawarizmi (circa 780 - circa 850). The manuscript is stored in Berlin, Staatsbibliothek, Landsberg 56, 77b-97b. Note that B was used by both al-Maghribi and al-Khawarizmi. However, al-Maghribi uses the circle zero (०) but al-Khawarizmi uses the Mashriki dot zero (٠) instead.
The slow death of B
Now once the B-glyph is registered in our brain as the symbol for ‘5', it should stayed registered even when it is rotated. In what follows, we show the gujarati ઇ rotated by \(15^\circ\), \(30^\circ\), \(60^\circ\), and \(90^\circ\). This is perhaps, how we evolve the B-glyph to the inverted heart-shaped ‘5' (۵, U+06F5. The See also the reversed open E in Latin script, ɞ, U+025Eclosed omega in Latin, ɷ, also looks like an inverted heart U+0277) in modern Persian/Sindhi keyboard. Transition from inverted heart to the modern Mashriki ‘5' (٥, U+0665) is easy, since all you need to do is just to de-emphasize the cusp.
ઇ
ઇ
ઇ
ઇ
۵
۵
٥
Evolution of arabic numerals Seyyed Hossein Nasr (1976) Islamic science: an illustrated study, World of Islam Festival Publishing Company Ltd, London, p. 78 (Figure 22)
Persian inverted heart-shaped fives in a \(6 \times 6\) magic square Seyyed Hossein Nasr (1976) Islamic science: an illustrated study, World of Islam Festival Publishing Company Ltd, London, p. 80 (Figure 23). Note that this magic square has some mistakes in column 1 position 4, column 2 position 3, and column 4 position 4.
$$\begin{bmatrix} 2 & 31 & 33 & 34 & 10 & 1\\ 29 & 18 & 21 & 24 & 11 & 8\\ 30 & \color{brown}{23} & 12 & 17 & 22 & 7\\ \color{brown}{5} & 13 & 26 & \color{brown}{19} & 16 & 32 \\ 9 & 20 & 15 & 14 & 25 & 28\\ 36 & 6 & 4 & 3 & 27 & 35 \end{bmatrix} = \begin{bmatrix}۲ & ۳۱ & ۳۳ & ۳۴ & ۱۰ & ۱ \\ ۲۹ & ۱۸ & ۲۱ & ۲۴ & ۱۱ & ۸ \\ ۳۰ & ۲۳ & ۱۲ & ۱۷ & ۲۲ & ۷ \\ ۵ & ۱۳ & ۲۶ & ۱۹ & ۱۶ & ۳۲ \\ ۹ & ۲۰ & ۱۵ & ۱۴ & ۲۵ & ۲۸ \\ ۳۶ & ۶ & ۴ & ۳ & ۲۷ & ۳۵\end{bmatrix}$$
A 13/14-th century metal magic square with Hindu-Arabic numerals (14 by 14 cm, 1.5 cm thick), currently in Shaanxi History Museum (陜西歴史博物館). It was unearthed by Xian train station construction work in 1957, near the site of the Residence of There were three of them: Manggala (r. 1272 - 1278), the third son of Kublai Khan; Ananda (r. 1278 - 1307), the eldest son of Manggala; Yerutömör (r. 1307 - 1332), the son of Ananda.Prince Anxi of Yuan Dynasty (安西王府遺址). Note that the loop in the B glyph used in this magic square is consistently not closed. This metal artifact shows that people still use the mirrored-B glyph to denote five in 14th century Yuan China.
$$\begin{bmatrix}
28 & 4 & 3 & 31 & 35 & 10\\
36 & 18 & 21 & 24 & 11 & 1\\
7 & 23 & 12 & 17 & 22 & 30 \\
8 & 13 & 26 & 19 & 16 & 29 \\
5 & 20 & 15 & 14 & 25 & 32\\
27 & 33 & 34 & 6 & 2 & 9
\end{bmatrix} = \begin{bmatrix}
۲۸ & ۴ & ۳ & ۳۱ & ۳۵ & ۱۰
\\۳۶ & ۱۸ & ۲۱ & ۲۴ & ۱۱ & ۱
\\۷ & ۲۳ & ۱۲ & ۱۷ & ۲۲ & ۳۰
\\ ۸ & ۱۳ & ۲۶ & ۱۹ & ۱۶ & ۲۹
\\ ۵ & ۲۰ & ۱۵ & ۱۴ & ۲۵ & ۳۲
\\ ۲۷ & ۳۳ & ۳۴ & ۶ & ۲ & ۹
\end{bmatrix}$$
Persian five in Malay orthography
Here, we show four examples in which the non-standard mirrored-B/inverted heart-shaped five was employed.
This is a relatively recent artifact in Pulau Bintan, on which the year of death of Tun Abbas (Bendahara Seri Maharaja of Johor Empire) was inscribed. Note that the Persian inverted heart-shaped (♡) five is used instead the modern Mashriki five.
Tuhfat al-Nafis, Terengganu Manuscript, p. 191: . . . yang disuruh Yang Dipertuan Muda itu lalu diikat dan didapatnya tangan. Kemudian lalu disuruh bunuh dikerat kepalanya dikirimkan Lingga kepada Baginda Sultan Mahmud di Lingga. Maka habislah kisahnya Lebai Tamat itu . . . al-hikayat kata orang . . . ceriteranya pada hijrah sanah 1225, pada lima belas hari bulan Zulhijah pada hari Khamis pukul dua belas maka Baginda Sultan Mahmud pun memanggil paduka adinda bagindanya Yang Dipertuan Muda Jaafar . . . Note that the ‘5' in 1225 is orthographically rendered as B, instead of the Mashriki single-loop five (٥). Given the fact the manuscript was paginated with the single-loop five, it is likely that the script did not appreciate that the numeral he copied was a five and the glyph in the parent manuscript was merely faithfully replicated.
The seal of Sultan Abd al-Rahman of Lingga (see A. T. Gallop 2019, Seal #910, p. 316). The seal reads: al-Wathiq bi Rabb al-‘Arsh al-Wadud al-Sultan Abd al-Rahman bin al-Sultan Mahmud | Sanah 1225 min Hijrah al-Nabi salla Allah 'alayhi wa-salam seribu dua ratus dua puluh lima tahun yawm al-Jumaat. Note that the mirrored-B five in this seal is rendered like ‘৪' (‘4' in Bengali script, U+09EA) or our modern 8 with two loops, rather than the traditional Persian mirrored-B.
Pengasas Kuala Lumpur bukan Sutan Puasa,bukan Haji Abdullah Hukum,apatah lg Yap Ah Loy.Pengasas sebenar adlh Raja Abdullah ibni Raja Jaafar.Beliaulah yang dianugerahkn Sungai Kelang dan seluruh jajahannya hingga ke Sg Lumpur oleh Sultan Muhammad.Buktinya adlh 2 pucuk warkah ini. pic.twitter.com/riYjaoQc0l
Sultan Abd al-Samad renewed/re-assertained Raja Abdullah's position as the Governor of Klang Valley on 18 August 1864 (the calendrical data in the enfeoffment letter says Thursday 1 pm, 16 Rabi al-Awal 1281). The year in the seal reads: 1275 (11 August 1858 < 1275 < 30 July 1859). Note that the number ‘5' in 1275 is written as a mirrored B (ઇ). When Raja Sulaiman (the father of Raja Mahdi) died, the land around the Klang River was earlier assigned to Raja Abdullah by Sultan Abd al-Samad's predecessor in 1266 AH (17 November 1849 < 1266 < 5 November 1850), partly because Sultan Muhammad was indebted to Raja Jummat (Raja Jumaat was the elder brother of Raja Abdullah, he was also the brother-in-law of Raja Abd al-Samad). Note that the ‘4' in Sultan Muhammad's seal is written as ۴ (instead of our usual Mashriki ‘٤'). The year 1241 is the first regnal year of Sultan Muhammad (16 August 1825 < 1241 < 4 August 1826). Sultan Muhammad's letter shows that the appointment of Raja Abdullah took place in 1849/1850 and not 1853 (the year traditionally assigned as the year of death of Raja Sulaiman). Sultan Abd Samad's letter shows that the succession kerfuffle was quieted down only in 1858/1859 although Sultan Muhammad vacated his seat in 1857.
從吉打 Lembah Bujang 布央谷開車回家，經過怡保的時候剛好是晚餐時間。 在麥當勞用過晚餐後，發現開車的我好像也有點睏了，於是決定在怡保睡一覺。我們把車開到 Bandar Meru Raya ，然後跟 Casuarina 要了一間房間。 隔天早我見小兒子辛円睡到很遲還不願意起床，就拿起手機給他照了一張相。 大太陽曬屁股還不起身嗎？ 原想給照片標上：阿円睡到日上三竿，大太陽曬屁股還不起身。但，住在我頭腦裡面的另外一個人問我： 三竿到底是幾點？ 於是我便上網查了一下該成語的出處：「日上三竿」應該是出自《 南齊書・天文誌上・日光色 》的一段話。《南齊書・天文誌》是南齊政府天文局官員根據每日的觀測日記整理出來的天文異象報告。《日光色》的第三個記錄是這樣寫道的： 永明五年十一月丁亥，日出高三竿， 朱色赤黃，日暈，虹抱珥直背。 這段話有三個部分。第一部分「永明五年十一月丁亥」標的是日期。第二部分「日出高三竿」說的是太陽的高度，也就是當時的時間。第三部分「朱色赤黃，日暈，虹抱珥直背」解釋的當時天文局官員觀察到的天象。 通常我讀文言文的時候都會在頭腦裡面把文字翻譯成英語。因為只有這樣，才能逼我自己將每個字都解讀出來。這段話譯成英語大概是： Sunday. December 7, 487. The shadow cast by the sun is three times the height of the pole. The colour of the sky is between red and yellow. Solar haloes and parhelia are clearly visible. 我們先說日期的那一部分。「永明」指的是南齊的 蕭宣遠 先生。蕭先生是在公元483至493期間做皇帝的。永明五年自然是落在公元487年。後面的「十一月」指的是農曆十一月，而「丁亥」是中國傳統天干地支計日系統的寫法，它是一種 60模 的寫法，例如：甲子 = 1、癸亥 = 60。所以，「丁亥」的值為24。 接著我們用 Reingold與Dershowitz 的方法把農曆日期換算成格列高曆。其結果是：公元487年12月7日（既該年的第341天，\(d = 341\)）。 根據日影我
如果你或你的公司不還稅， 內陸稅收局 的人就會寄一封公函來罵你並跟你討錢。 在馬來西亞，所有的政府公函，都會印上 Urusan Seri Paduka Baginda 的字樣。「Urusan Seri Paduka Baginda」其實是延續英國人 On His Majesty's Service 的傳統。「 Seri Paduka Baginda 」這三個字的英語是「His Majesty」或「Her Majesty」，而「Urusan」則是「Service」。 現代英國郵遞系統的原型是愛德華四世國王 Edward IV (1461-1483)設計的，他為了加快情報的傳遞速度，在大概每30km就設了一根柱子(post)和一匹新馬。這樣，情報的傳遞便能達到約2 m/s。 J. C. Hemmeon在1912年出版的《The history of the British post office》是這樣寫道的： A somewhat different style of postal service, a precursor of the modern method, was inaugurated by the fourth Edward. During the war with Scotland he found himself in need of a speedier and better system of communication between the seat of war and the seat of government. He accomplished this by placing horses at intervals of twenty miles along the great road between England and Scotland. By so doing his messengers were able to take up fresh horses along the way and his despatches were carried at the rate of a hundred miles a day. 500年前2 m
Water disruption at Pangkalan Lumpur On 29 March 1877, Captain Yap Ah Loy wrote a Arkib Negara 1957/0000387 letter to Captain W. B. Douglas (r. 1875 - 1882, Acting Resident of Selangor) to relay a water-related grievance at Pangkalan Lumpur tin mine. This letter is important because it contains several important data points: Yap Ah Loy addressed himself with the Indic title (श्री इन्द्र प्रकाश विजय भक्ति = Sri Indra Perkasa Vijaya Bakti), and This shows that back in 150 years ago, it was perfectly reasonable for Malay courts to install their subjects with Indic titles and decorations, similar to the practices recounted in Sejarah Melayu. However, the way Yap addressed himself was not consistent, for instance, in 1881, he called himself Kaptan Cina Kuala Lumpur and not Kaptan Klang dalam Kuala Lumpur but he used his Indic title consistently. See Arkib Negara Document Number 1957/0001366W . called himself Captain Klang in Kuala Lum
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
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