Islamic Civilization Heritage: Mathematics

When Europe was entrapped in the darkness of the Middle Ages, other cultures were instead shining in the light of civilization. The medieval Islam in particular was glowing for its numerous achievements in science and technology. One of the subjects the modern world is much indebted is mathematics as the backbone of technological development. 

The relic of the Muslims contributions can be embedded to the very fundamental of mathematics which is the numbering or numeral system. Prior the Middle Ages, numeral systems were mostly developed from letters or alphabetical symbols. Evidence can be seen in the Chinese, or the Roman systems. The other famous system is the Babylonian sexagesimals -numerals based on ‘sixtieth’ as a central- which has been prevalently used in astrology and astronomy (see Figure 1). Along with cultural progress, those systems prove to be impractical in performing advanced mathematical operations. Imagine how complicated the work is, in the Roman systems, when we want to multiply DXXX (530) with XXXIX (39). Even though there is an existing method to do, the use of Roman system in mathematical manipulations is far from being fun. Using a method taught in nowadays schools, most will find it simple to give 20670 as the solution. 

  Figure 1. The sexagesimal presented in Arabic letters. Note the first four letters (reading from right to left); ‘alif’, ba’, ‘jim’ and ‘dal’ construct the word abjad, a term for a less known numeral system which still applies in some Arabic cultures (taken from: Islamic Science and Engineering, by Donald Hill)

The simplification of the numeral system was initiated by Muslim scholars in the 8-9^th century AD during the Abbasid Baghdad period. Having adopted a system from Brahmi culture, Muslim mathematicians, notably Al –Khawarizmi¹ and Al – Kindi², introduced a much simpler system of decimal or numerals based on ten symbols. The Muslims also refined the system with the promotion of ‘zero’ symbol which enables us to distinguish easily between, for instance 5, 50 and 500. The Hindu - Arabic decimal system, later known as the Arabic system however, did not flourish quickly since it was considered strange, even among Muslims at that time because of their more accustomed to the Babylonian sexagesimal. In Europe the system was unrecognized not only due to sentimental prejudice, but also because the Roman system was sufficient to carry out simple calculations in the European daily life. It had taken several years since its introduction by Al – Khawarizmi before Arabic system came into practical applications. In Europe the system was popularized by Leonardo Pisano or Leonardo Fibonacci in the 1200s, after returning home from his learning journey in the Islamic lands. Since 1400s, the Arabic numeral system (see Fig. 2 for evolution description of the system) has become a common choice to represent scientific ideas and theories.

 Figure 2. Illustration of the Hindu – Arabic numeral systems evolution (diagram is adapted from “Pathfinder: The Golden Age of the Arabic Science” by Jim Al – Khalili of the University of Surrey, UK).

Together with the progress of the subject, particularly in arithmetic and algebra due to the swift and simple Arabic numerals, the medieval Muslims contributed further with development of another mathematical branch: trigonometry. The idea of trigonometry was certainly not new as some principles could be traced back to the ancient Greek and Hindu cultures. However, it was the medieval Muslims who complemented it with the invention of trigonometrical function of tangent, cotangent, secant and cosec. Further, the Muslims employed them extensively in various scientific fields.

As an example of integrated application of mathematics, we may pay a visit to a remarkable work of the legendary Muslim scholar Muhammad Al – Biruni³ on the estimation of the earth circumference. The study on the global circle was motivated by an interest to determine the vast empire the Muslims had to administrate, thus enabled them to understand the portion of their realms in the global map. More importantly, the data was essential to determine the qibla, a fixed place Muslims should face in the daily prayers. Before Al – Biruni, a Greek scientist Erastothenes of Cyrene, proposed a method on the subject by measuring the distance between two places which produced few degree of difference on an object’s sun shadow. Once the distance and the angle differences could be determined, full circle circumference could be calculated from the proportional ratio of angle and distance (Figure 3).

 

Figure 3. Simplified illustration of the Erasthotenes method to determine the earth circumference. Syene or Aswan was selected as starting point of observation for its location around the Tropic of Cancer, thus at midday during the summer solstice the sun is relatively vertical /overhead to the town.

The principal idea of Erastothenes was simple but in practical it was too difficult to apply. To produce 1^o difference on sun – ray shadow for instance, an experimenter would need to relocate a distance of hundreds of kilometers from his/her original position. The accurate distance measurement between both points had been problematic as there was no reliable method to calculate such a long range. Scientists then carried out an approach by counting a number of a person’s pace between two observation stations as a method for distance measurement. This practice certainly has large margin of errors due to several uncertainties, such as experimenter physical conditions, weather, and other external factors. No wonder, Erastothenes method produced different results from one experimenter to another. (Erasthothenes suggestion of observation between two places of Alexandria and Syene (now Aswan) in Egypt obtained 7.5^o of difference, turns out to be approximately 800 - 900 km of distance in modern calculation).

Figure 4. The Al – Biruni’s method of the earth circumference measurement:

(I) determination of the height of the mountain from two points of 1 and 2

(II) determination of the earth radius from an angle of observation of ϕ (observer at A position)

Al – Biruni proposal was much simpler in idea as well as implementation. Using a large astrolabe, Al – Biruni picked two places with known distance, approximately 100 m, at the same sea level and measured angle of elevation of both to the top of a mountain. This step provided Al – Biruni the height of the mountain which he used to finalize his calculation. Climbing up to the mountain, he measured the angle of the sight from the mountain top, dipping far down to the horizon. Those four parameters, three angles of observation and one height of the mountain, were obtained and then correlated with trigonometry and simple algebra to determine the radius of the earth. The data of radius eventually enabled Al – Biruni to calculate the earth circumference (See Figure 4). The work of Al – Biruni in the 10th century was phenomenal as his estimation found to be 40233 km (25000 miles) for the earth circumference, less than 1% difference from modern calculation at 40075 km (24902 miles).  

There are still numerous studies in which mathematics was employed as references of the Islamic civilization accomplishments. Those may be found in the excellent works of: Ibn Haytham⁴ on optics and astronomy, Al Tusi⁵ and Ibn Shattr⁶ on celestial movements (by the way, Tusi and Shattr mathematical models were very influential on the development of the 16^th Century AD Copernicus heliocentric theory), Jabr Ibn Hayyan⁷ and Al Razi⁸ on chemical processes (metallurgy, distillation, calcination, crystallization, extraction), Ibn Sina⁹ on astronomy and musical mathematics, Al Jazari¹⁰ and Banu Musa¹¹ on automatic devices, Ibn Mu’adh¹² in estimating the height of the earth atmosphere and Al-Battani¹³ in determining number of days of a solar year. All become factual examples of the civilization milestones from the Islamic world which at one time was very productive in science and technology, not only for the sake of curiosity but also in the effort to embrace the grandeur of the nature.

 Notes:

1) Muhammad Al – Khawarizmi (c.a 750 – c.a 850), was born and brought up as a Zoroastrian. There is no clear record actually, whether he converted to Islam. However, in his most famous book of Al Kitabul Muhtashar fii Hisab Al Jabru wal Muqabbala (The Compendious Book on Calculation by Completion and Balancing) -the first book on mathematical operation of Algebra- Al–Khawarizmi, known also as Algoritmus in the West, began his writing with Bismillahirrahmanirrahiim, or ‘In the Name of The Almighty God, the Most Gracious and the Most Merciful’, a line commonly written by muslim authors. Al – Khawarizmi’s step by step instruction to solve mathematical equations is immortalized in a term called algorithm.

2) Yusuf Ibn Ishaq Al Kindi c. 801 – 873 AD was an Arabic philosopher, born in Kufa, currently a small suburb of Najaf in modern Iraq. Al – Kindi is known as one of great philosophers the World has ever witnessed. Al – Kindi was a polymath, writing at least 200 books on various subjects; philosophy, mathematics, astronomy, medical science, pharmaceutical, psychology, chemistry and zoology. Al - Kindi was also remembered as an exquisite musician. 

3) Abu Rayhan Muhammad Ibn Ahmad Al – Biruni, 973 – 1048 was a Persian polymath mastering mathematics, astronomy, geography, linguistics and philosophy. He is well known as the Father of Geodesy. Al – Biruni was also an avid historian, famous for his book Tarikh Al Hind or the History of the Hindu Land (India).

4) Abu Ali Al Hasan Ibn Hasan Ibn Al – Haytham, born in Basra c.a. 965, was a polymath, a master of mathematics, astronomy, physics, philosophy and optics. Ibn Haytham, sometimes also written in other Romanized Arabic spelling as Ibn Haytsam, is known as Alhazen in the West. He has been famous for his book Al Kitabul Manazhir or the Book of Optics/Visions, and Al – Shukuk ala Batlamyus or The Doubt on Ptolemy’s (theory of celestial movement).

5) Nashiruddin Al – Tusi, or Muhammad Ibn Hassan Al –Tusi, 1201- 1274, was a Persian polymath with expertise in mathematics, astronomy, physics, theology and chemistry. Al – Tusi is well known for his theory of Al–Tusi couple, a significant correction to the hypothesis of Ptolemy on planetary motion.

6) Ala Al-Din Abu'l-Hasan Ali Ibn Ibrahim Ibn al-Shatir (1304 – 1375), was an Arabic mathematician and engineer. Ibn Shattir was a pray – time keeper in the Grand Mosque of Umayyad in Damascus, famous for his versatile sundial to determine prayer-time in the medieval Islam. Ibn Shattir also reformed Ptolemy’s theory on celestial motion. The mathematical model proposed by Al-Tusi and Ibn Shattir has been closely similar to that of Copernicus in 1543.  

7) Jabir Ibn Hayyan, c.a. 721 – 815, was a polymath living in the time of Caliph Harun Al – Rashid of the Abbasid Baghdad. Jabir was among the pioneers to revolutionize alchemy into chemistry through experimental approach. Jabir is remembered as a productive scholar, writing at least 100 books on various topics. At least, another 3000 books and manuscripts were written bearing the name of Jabir (latinized as Geber) as attribution to Jabir’s authoritative knowledge from scholars who came after him.

8) Muhammad Ibn Zakariyya Al – Razi, 854 – 925 AD, was another outstanding Muslim polymath in the time of the Abbasids. He was well known for his expertise in medicine, chemistry, mathematics and philosophy. Al – Razi continued the approach Ibn Hayyan had done several decades earlier, in promoting quantification and experiments to chemistry and chemical processing. Al – Razi was also a renowned medical doctor, a pioneer in the establishment of hospital.  

9) Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Al-Hasan ibn Ali ibn Sina, 980 -1037, was an Uzbek born scholar. Ibn Sina was a genius, authoring approximately 450 books on wide range of subjects notably medicine, mathematics, chemistry, philosophy and arts. His multi-disciplinary expertise is often overshadowed by his famous book  Al-Qanun Fil Tibb or The Canon of Medicine, the primary reference for medical practices in the Middle – East and Europe until around 1700s.  

10) Ismail Ibn Razzaz Al-Jazari, 1136–1206, was a Muslim engineer, mathematician, and artist.  Al – Jazari, commonly attributed as the Father of Robotics, is well-known for his automation concept in water - pump and water - clock. His gigantic elephant water – clock has been remembered as one engineering wonder, up to this day.

11) Banu Musa, c.a. 803 – 875 or the Moses Brothers: Muhammad Ibn Musa, Ahmad Ibn Musa and Hasan Ibn Musa, were prominent engineers in the time of the Caliph Abdullah Al Ma’mun Ibn Harun Al Rashid of the Abbasid dynasty. Banu Musa were among scholars trusted by Al – Ma’mun to develop automatic devices; such as pump, fountains and reading lamp. Banu Musa also wrote dozens books on astronomy.

12) Muhammad Ibn Mu’adh Al–Jayyani, 989 – 1079, was a Qadi, or Islamic Law judge in the time of Andalusian Islam in Spain. Ibn Mu’adh was a prominent scientist in the field of mathematics particularly in spherical trigonometry. 

13) Muhammad Ibn Jabir Ibn Sinan Al-Battani, 858 – 929, was born in Harran, southern part of modern day Turkey. Al – Battani was an expert in astronomy and mathematics, well – known for his expansion of trigonometry function of sines and tangent. Al–Battani was the first person to revise Ptolemy theory on solar apogee. The work of Al-Battani was influential to medieval European scientists such as Copernicus, Brahe and Galileo.  

The Champion Forever

In 2007 Bert Randolph Sugar, a prominent boxing writer, released his list of top ten heavyweight fighters of all time. Not much different from other versions, Sugar ranked Joe Louis and Muhammad Ali on the top two, followed by other names: Jack Dempsey (3), Jack Johnson (4), Gene Tunney (5), Rocky Marciano (6), Ezzard Charles (7), George Foreman (8), Joe Frazier (9) and Larry Holmes (10). Sugar’s list invites many comments from boxing fans due to its apparent subjective. Champions in 1940-1950s got higher ranks than those of any other era. The list is normally understood as Bert Sugar grew up to watch his old timer heroes fighting in the ring. However, the list would be completely different if Sugar were born at later time. For many boxing fans, the name of top heavyweight fighters, from no 1 all the way to number 10, is one and only Muhammad Ali.

Ali was indeed a unique person inside and outside the ring, captivating public attention through his skill and charisma. Instead of having constant stance like many of his predecessors in the heavyweight division, Ali opted to fill his fighting-style with diligent footwork, slippery body weaving, dancing and jabbing.  His style was quite unusual for the fighters in the upper divisions to perform. Ali’s style closely resembled fighters in the middleweight divisions, such as the dancing master Willy Pastrano or the flowery and flamboyant Sugar Ray Robinson. With the style which was later coined as ‘float like a butterfly and sting like a bee’, Ali, formerly Cassius Clay Jr, captured the world title from Sonny Liston in 1964, and continued to dominate the division until 1967. In his second career spell from 1970 till  1980s, Ali did not dance much as he grew older. But, boxing fans was entertained with his body strength, various tricks and numerous unorthodox strategies to cope with younger, and stronger opponents. That was obviously seen in his famous ‘the rope-a dope’ style. Astonishingly, a less danced Ali was still stinging, combined with his mature boxing skill which harvested his other title belts in 1974* and 1978**.

 

Outside the ring, Ali was a social activist. He embraced Islam in 1964 and participated in social movements for the minorities, in particular for the African - American communities. He was once condemned by American conservatives when he controversially refused to join military service for the Vietnam War. The refusal costed Ali's title strip in 1967. But his decision was highly appreciated among African-Americans as a symbol of struggle in the American civil movement. Along with that, Ali also gained popularity in Asia and Africa as a symbol of optimism from the developing worlds emerging society.

There is an interesting story repeatedly told when Muhammad Ali was about to fight the world champion George Foreman in 1974. While most world boxing analysts and journalists picked Foreman as their favorite, Asian and African public had their confidence on Ali to win the fight. When they were asked why they supported Ali, the reason was quite simple, even sometimes it was amusing. Some said they bet for Ali because he was their hero while they were younger. But some were more mythical. Many people in Indonesia, for instance, opined that:

 

“The name of Muhammad Ali was taken from the name of our beloved prophet (Muhammad) and the name of a brilliant muslim leader and commander (Ali, the 4^th Caliph in Islamic traditions). When both names are combined, none in this world can be more superior to that”

 

The reason might sound baseless and ridiculous to experienced boxing experts. However, it was Ali’s fans whose eventually got the last laugh. Ali dramatically defeated Foreman in a legendary fight called 'The Rumble in the Jungle' to regain the title he lost several years before.

After retirement from professional boxing in 1981, Ali was still active in several social activities. He is remembered as one of the great gentlemen whose life had been dedicated to humanity. To most, his remarkable life is memorable, as his name continues to inspire the world through his spirits, love and courage. Despite his physical disadvantage in his later life, Ali seemingly tried very hard to revive the figures he loved most and from which his name was derived: Muhammad the prophet and Ali the caliph. And due to his dedications, Ali is still people’s idol and hero, lingering in the minds of both boxing fans and global community, as their very fine champion forever. 

Note: 

*) George Foreman vs Muhammad Ali, 30 October 1974, the Rumble in the Jungle, contested in Kinshasha, Zaire (now the Democratic Republic of Congo). Ali won by a knock-out in Rd 8 (pictured in the headline photo).

**) Leon Spinks vs Muhammad Ali, 15 September 1978, was staged in New Orleans, Louisiana. Ali won a decisive 15-rounds bout to become the 1^st fighter to win 3 times the world title in the heavyweight division  

 

 

Lukisan Cat Air Brasil (Aquarela do Brasil)

Karya ternama sering dihasilkan dari suatu spontanitas saja. Seperti halnya sebuah komposisi ciptaan seniman musik dari Negeri Samba, Ary Evangelista Barroso. Suatu malam sekitar pertengahan 1939, Barroso dan istrinya berkeinginan untuk pergi melihat-lihat gemerlap Kota Rio De Janeiro. Kesibukan sehari- hari sebagai ahli hukum dan pengisi tidak tetap acara musikal untuk radio-radio lokal di Rio telah membuat fisik dan batinnya lelah. Tetapi, kala itu apa yang dimaksud tidak kesampaian karena hujan lebat mengguyur areal Carioca sejak sore hari. Hujan tak kunjung reda membuat Barroso berdiam di rumah, ditemani istri dan saudara-saudara iparnya. Sembari saling melempar canda dengan keluarga, Barroso menangkap suara – suara dari gemericik hujan membasahi pepohonan di sekitar rumahnya sebagai inspirasi akan kekayaan Alam Amazonia. Secara sentimental pula, Barroso menganggap apa yang ditemui sebagai sebuah lukisan air hadiah dari Tuhan untuk menenteramkan kebosanan dalam hatinya. Spontan Barroso beranjak, dikutak-katik piano tempat ia biasa menghibur diri, dirangkai baris-baris kata dalam irama. Dalam tempo singkat, tumpahan kekaguman Barroso terwujud dalam lantunan rampak yang ia beri nama Aquarela do Brasil, atau Lukisan Cat Air Brasil.

Akan tetapi, cerita manis Aquarela do Brasil tidak serta merta terjadi setelah lagu itu dilepas di pasaran. Saat awal-awal diperkenalkan, lagu ini hanya muncul di pertunjukan-pertunjukan setempat, tanpa mampu menembus kalangan elit seniman secara nasional. Lagu tentang Lukisan Brasil kerap dituding sebagai titipan dari Getulio Vargas, Penguasa Brasil yang saat itu sangat otoriter. Secara kebetulan memang, Lukisan Brasil sering dipakai oleh Pihak Pemerintah Brasil dalam kampanye maupun promosi berbagai kegiatan untuk melanggengkan kekuasaan. Sudah lazim pula, penguasa diktator umumnya punya kebiasaan untuk memakai atribut fanatisme kelewat muluk terhadap golongan atau partai politik tertentu, ditambah bumbu nasionalime dalam menjalankan kebijakan sehari-hari. Namun demikian, semua suara miring tersebut dianggap sepi oleh Barroso yang tetap rajin mengusung Aquarela do Brasil dalam banyak penampilan keseniannya.  

Bintang terang mulai tampak dari Aquarela do Brasil, saat Perang Dunia II pecah. Untuk mengimbangi propaganda yang dilakukan oleh Pihak Poros (Axis) pimpinan 3^rd- Reich di Jerman, dunia industri hiburan Amerika Serikat turut aktif dalam membuat film-film bertemakan persahabatan antara negara-negara Amerika Utara dan Amerika Tengah - Selatan (Latin). Seniman film kartun di Disney kemudian membuat Film Saludos Amigos (1942), yang bercerita tentang perjalanan wisata tokoh-tokoh kartun Disney ke Amerika Latin; Peru, Chile, Argentina dan Brasil. Dalam screenplay yang menggambarkan Brasil, lagu Aquarela do Brasil terpilih menjadi soundtrack. Selepas Saludos Amigos, karya Barroso menjadi terkenal, menyebar ke banyak negara di seluruh dunia. Lagu Lukisan Cat Air Brasil diputar berkali-kali di radio-radio sebagai sarana hiburan penurun tensi dari masa – masa penuh gejolak selama perang besar berkecamuk. Seusai Perang Dunia II, lagu ciptaan Barroso tetap populer, bahkan direkam ulang oleh ratusan artis penyanyi dan grup musik dalam berbagai bahasa. Di acara-acara rakyat, seperti halnya Carnaval do Brasil, atau saat Selecao tim nasional sepakbola Brasil bertanding, Aquarela do Brasil sering dinyanyikan beramai-ramai sebagai lagu nasional, setara dengan Lagu Kebangsaan Himno Nacional Brasilero.

Aquarela do Brasil rekaaan Barroso ini disamping menarik, juga mengandung banyak pesan. Di dalam rangkaian nada rancak yang kemudian digolongkan dalam genre Samba Exaltacao tersebut, Barroso mengungkap harapan tentang kehidupan yang egalit dimana semua ras, baik kulit putih maupun berwarna hidup berdampingan dalam harmoni alam raya. Pesan Barroso ini sangat kuat menembus perjalanan waktu, karena sekalipun dipopulerkan pula oleh pihak-pihak lain dengan berbagi warna, versi asli Aquarela do Brasil masih tersimpan abadi dalam ingatan para pecinta seni di seluruh dunia. Artis papan atas Hollywood era 50-60-an seperti Bing Crosby, Rosemary Clooney atau Frank Sinatra, misalnya, sempat mengusung adaptasi Aquarela do Brasil dalam Brazil yang lebih romantis berisi tentang kerinduan asmara seorang pengembara. Tetapi bagi kalangan orang kebanyakan, versi-versi turunan tersebut tidak terlalu berkesan dan belum sanggup menggusur versi asli milik Barroso. Aquarela do Brasil yang asli memang lebih humanis, berisi hakikat kehidupan manusia yang selalu ingin hidup damai, berpadu pujaan akan keindahan lukisan alam hasil coretan mengagumkan dari Sang Maha Kuasa.