The existence of mathematical sciences in the Malayonesian mould is presented theoretically based on a popular definition of mathematicl sciences, namely “problem solving”. There are 7 grades of membership of “knowledge in our own mould”: the highest is a solution of the original Malayonesian problem in the Malay language by anybody, and the lowest is a solution of a foreign problem and in a foreign language (a non-Malayonesian language), but by the people live in the Malayonesia). A focus is given to the Malayonesian mould which involves the concept of Malay and Malayonesian region and its civilization since the 2nd century AD in Kampuchea (the Funan-Malay Kingdom) and Vietnam (Champa-Malay Kingdom), followed by the post-Hindu-Buddhist Malay World civilizations since the 12th century until now. Concrete existence of elements of pre-Islamic and early Islamic Malay World mathematical sciences are presented in 11 categories from the wold oldest decimal number and numeral system (containing zero) to the manifestation of the advanced level of mathematical sciences in architectural, shipping and armament technologies, and chemistry each of which were ahead of the other parts of the world at the time. Criticisms and/or innovations on some elements of contemporary mathematical sciences are presented based on Islamic-Malayonesian mould. The topics are logic, set and probability theories, group theory and its extension, knots theory, Einstein and quntum theories, concepts of optimum, financial-management mathematics, and management and leadership theories.
Introduction
Despite the fact that the non-neutrality or cultural biasedness of science has been circulated through out the world at least since 1960’s, particularly through the work of Kuhn (1962/1997), Nasr (1964/1992, 1968/1986), al-Attas (1978/1981), al-Faruqi (1982/1991), Ijmalis (1990’s) and four institutions namely IIIT, USA (1982), IA, UK (1987), MAAS, India (1990), and ASASI, Malaysia (1978), a mathematical science knowledge is still very much considered by many as an objective knowledge and hence should be universally accepted without any reservation based on human values. Perhaps this situation can be understood due to the fact that the arguments put forward by those scholars and members of the four institutions above did not envolve mathematics directly until only early 1990’s through the work of Shaharir & Abdul Latif (1987/1992, 1988), Stwertka (1987), Dauben (1992), Gillies (1992), Shaharir (1992), Gross et al. (1996) and Hart (1996). A more profound reason for the slowness is that the subject has not reached to the level of a “normal science” (according to Kuhn’s nature of science), and hence it is yet to be recognized as a national thrust area of research. This is an irony especially for Malaysia, because the expression “progress in our own mould” or “develop in our own mould” is stated in the famous “Wawasan 2020” (“Vision 2020”) in 1991 (in the 6th Malaysia Plan) and has become a popular dictum since then; alhough some of the policies lately seem to contradict that vision.
It is not our intention here to repeat any of those historical and philosophical arguments presented by the above mentioned scholars and institutions. Our purpose is to present the status of the actual development of the subject so far in mathematical sciences. However, for this introduction, we would like to explain the meaning of “mathematical sciences in our own mould” by just simply appeal to a popular image of mathematical sciences, namely “solving problems”. “Our own mould” is our language, our culture, our way of life, our philosophy, our values and our religion. Therefore, if we think mathematical sciences are those knowledge(s) which come from solving problems, then it must necessarily be in our own mould if the problems were originally ours and most of the ideas in solving them were also ours, and were expressed in our own language.This is of course the highest grade of “knowledge in our own mould”. Indeed “our own mould” is subjective and thus “knowledge in our own mould” is a fuzzy set. In this paper “Mathematical sciences in our own mould” simply means “the Malay-World mathematical sciences”. We have discussed the meaning, principles, methodology and the scope of a Malay-World knowledge earlier (Shaharir 1990, 1995/1997, 1997/2004, 2000, 2003a, 2004, 2006a) and hence we just briefly stated here only in different terms, namely in terms of a fuzzy set. Accordingly, the highest grade of a Malay-World knowledge is
(G1) an Islamic-Malay-value-laden knowledge expressed in the Malay language and the subject matter is originated from the Malay World. The Malay language here means the Malaysian, Indonesian, Bruneian, Singaporean Malay etc in the Malay World)
Other grades are as follows (in descending orders):
(G2) A non-Islamic-Malay-value-laden knowledge expressed in Malay language and the subject matter is originated from the Malay World. (Note that non-Islamic is not equal to un-Islamic).
(G3) Other value-knowledge expressed in Malay language.
(G4) Knowledge expressed in the Bahasa Rumpun Melayu (a Malayonesian/ Austronesian/language of a Malay ethnic group or the Malay World)
(G5) The same as in the first category but a translation work.
(G6) The same as in the second category but a translation work.
(G7) The same as in the third category but a translation work;
(G8) An Islamic-Malay-value-laden knowledge expressed in a non-Malayonesian language by citizen(s) of a member of the Malay World (MW).
(G9) A non-Islamic-Malay-value-laden knowledge expressed in a non-Malayonesian language by citizen(s) of a member of the MW.
(G10) Other knowledge expressed in a non-Malayonesian language by citizen(s) of a member of the MW. (the lowest grade)
A knowledge obtained from solving a problem using our own data to fit an existing foreign model is at most constitutes our own knowledge of the third category. It is important to realize also that “knowledge in our own mould” or specifically here, “Malay-World knowledge” can be universal once the knowledge is acceptable by others outside the Malay World. After all this have had happened to the the pre-Islamic Malay-World knowledge as the work expressed in Kunlun (ancient Malay) were seek by Indians, Chinese and Japenese scholars in 500-1200AD as mentioned by Muhammad Alinor (2004, 2005). Even now there are some mathematical writings (non-mathematical are much more) in Malay which have been translated or referred to by scholars outside the Malay World. We believe that this would happen much more if our knowledge proves to be more original and useful. After all the present mathematical sciences (assumed to be universal) were originally developed in a local mould mostly in Europe and America or what we generally called it as the Western mould.
In this paper we show how far the pre-Islamic era of the Malay-World had developed world class mathematical sciences and at what extent the present Malay-World (Islamic, non-Islamic) values have been contributing in a development of new mathematical sciences for the last 10 years (since the articulation and the struggle of some scholars towards dewesternisation or desecularisation of scientific knowledge under various names: ethnoscience, ethnomethodology, Islamisation of knowledge, humanization of science, and indigenisation of knowledge). Here, we show that there have been indeed some development in mathematical sciences during the last decade toward realizing the dream and struggle of the above such scholars, institutions and many others who believe in the virtue of a nation which has been developing or have had developed in her own mould. However, first we thought it would be useful to present the meaning of the Malay World itself (Details are found in Shaharir 1998/2000, 2003a).
1. A Brief History of the Malay World
As far as national language is concerned, Malay language, the lingua-franca of the Malay World (MW) is ranked at least 4th (considering Indonesian population alone, according to world population listed by the Wikipedia: first Chinese, followed by India, and the United States of America). As a language for a Muslims nation-state (an Islamic language) Malay (considering only Indonesian) is certainly the top Islamic language in the world. In terms of most widely spoken languages in the world, we believe that the Malay language is in a position high than the nineth as stated in several websites (first Mandarin, followed by English, Hindi, Spanish, Arabic, Russian, Portugese and the eighth, Bengali). In fact according to Graddol (2004), there were (based on a survey in 2004) about 300 millions people of the MW (and Malay diasporas and others?) who used Malay as their lingua-franca, which would put in the 4th or 5th position in the world rank of most widely used languages. It is interesting to note also that Graddol predicts that English may not be a dominant language in the future! He also states that Malay is the third fastest growing language in the world (after Chinese and Spanish).
It is important to agree on the meaning of the MW because “our mould” in this paper means the mould of the MW. In the 17th and 18th centuries, the Western scholars refered the MW in various other names such as notably the Indian Archipelego, Asiatic Archipelago, Eastern Archipelago, Indo-Australian Archipelago, and the East Indies (and equivalently in other European languages, except the French scholars who had also refered this region as Archipel Malasien and Malasia which were translated into English as Malaysian Archipelego and Malaysia respectively). Other European scholars in the 17th and 18th century refered the present MW as Indunesia/Indonesia and Malayunesia. All of these names were slowly replaced by the Malay Archipelego in the late 18th century and later the MW to include a wider region. Before the Western colonials came to the East in 15th century, this MW was known in various names: Suvarnabhumi/ Swarnabhumi, Suvarnadvipa/Swarnadvipa, Yavadvipa/Javadhipa and Dvipantara by the Indians; Ye Diao (=Javadhipa) by Chinese; Chrys Khrosonesos, Chry Insula, Iabadio dan Yawadvipa by the Greeks and the translation of it in other European languages such as Aurium Chorsenesis in Latin and Golden Khorsenene/Korsenes/Chorsenes in English which means the Golden Archipelago; and the Arabs have referred it as Jawa or Jawi since they have in contact with the people from this part of the world in as early as the Greeks had (in early first century) and they still use it until today. At the same time the people of this region themselves used to called it as Nosa Kanca, Nosa Kancana, Nosa Koncana or Nuso Koncono (the pesent form would be Nusa Kencana, literally means Land of Gold, or Golden Land) which is the same meaning as Swarnabhumi and Yavadhipa, and hence it may be speculated as the oldest and the original name of this region. As far as the name Nusantara (presently still popular especially among intellectuals, cultural groups, creative writers and artists), originally the name was officially declared by the greatest ruler of the Majapahit Empire in 12 century, Hayam Wuruk and his well known Prabhu/Prime Minister, Pateh Gaja Mada.
During their struggle for freedom from the Western colonials in the 20th century, the Malay-World leaders have proposed various names for their dreamed unified land which includes Malayanesia/Melayunesia, Indunesia/Indonesia, Malaya/Melayu Raya, Indunesia/ Indonesia Raya, Petani Raya, and Nusantara but failed to materialize. In early 1960’s, as the feeling of reunification was getting high, the idea of forming a union of the Federation of Malaya (Persekutuan Tanah Melayu), Philippine and Indonesia to be named as Maphilindo was mooted but ended with the war of attrition between the newly formed nation Malaysia and Philippine on the historical issue of Sabah and a declared Confrontation between Malaysia and Indonesia on the issue of the formation of Malaysia. Again after the end of the Malaysia-Indonesia Confrontation 1965 it was suggested to form Malindo, an abbreviation from the name of the two countries, but only have materialized in the form of language reunification by declaring the common system of spelling 1972 and the formation of a joint committee for the common standardization of the two languages especially the scientific terminologies known as Majlis Bahasa Indonesia-Malaysia (MBIM), The Language Council of Indonesian-Malaysia, which is still functioning today with a larger memberships which includes Brunei as a full member and Singapore as an affiliate member since 1990’s, and hence the name of the council has been changed to MABBIM to include Brunei. In 1970’s a well known Malay-World scholar, Sutan Takdir Alisjahbana (an Indonesian citizen but held a professorship in Malay study at UM for a long time since 1960’s) had suggested a new name for the MW as Bumantara since Nusantara was not and has not been accepted by Indonesian government for a historical reason (for excluding Jawa in the original intention of coining Nusantara) but once again it was not responded well by any of the nations concerned. In 1987 the author refers Malindopura in the Introduction of first edition his book (Shaharir 2000 for the 2nd ed.) but obviously had received a similar fate; and recently he made yet another new suggestion, Pascabima (Shaharir 1998) after the name all the ancient Malay kingdoms, Funan-Cenla and Campa, and nation-sates of the present MW. Perhaps the best name is still Nusantara but we still refrain ourselves to use it here, even though it is not unusual to witness another new name of this region, the Indonesian Archipelego, since more than half of the Malay World is in fact, since 1945, known as Indonesia. Let us briefly browse through the nature of the MW before this century.
In 1845, a British ethnographer, Earl defined the Malay Archipelago in a paper presented at the Royal Geographical Society UK, as a region in South-East Asia which includes Peninsula of Malaysia, the present South Thailand (the Kingdom of Petani), up to Tenasserim and Nicobar Islands in the West, Philippine in the North, and Solomon’s Island and beyond New Guinea (now Niugini) in the East. In 1863 Wallace, a well known British natural scientist, while he was doing reaseach in the South-East Asia, in his paper “On physical geography of the Malay Archipelego”, dalam J. Royal Geographical Soc. XXXIII: 217-234, defines the Malay Archipelego as almost a triangular region in South-East Asia which includes Nicobar Islands to the North-West, Solomon’s Islands to the South-East, in the North from Luzon to Rotti, and to near Timor Island in the East. He also characterize the Malay Archipelago simply as the region between the South-East Asia and Australia, and separates the Indian Ocean and the Pacific Ocean. In 1869, Wallace really became the man who was responsible for popularizing the name of Malay Archipelego through his famous book and a best seller for centuries since it was first published 1869, “The Malay Archipelago. The Land of Orang-Utan and the Bird of Paradise: A Narrative of Travel, with Studies of Man and Nature” . The book was reprinted and reedited numerous times and the latest that we know of is published by Graham Brush, Singapura 2004 (with a new introduction), interestingly reviewed by Mat Rofa (2006). Incidently, this book easily would become one of a great book of the Malay-World biology if it were translated into Malay any time. As it is, the book is fittingly recognized as a great book of English biology in the same category as the the Origin of Species by Darwin; and the Nobel Prize winning books “Among the Believers” 1981 dan “Beyond Belief “1998 by Naipul (an Indian-Trinidad origin but became British citizen, so appropriately regarded as a British Nobel Laureate even though the materials of the books are regarding the people of the MW).
Meanwhile French scholars since early 18th century have been used the words Archipel Malasien (Malaysian Archipelago) and Oceanien et Malasia (Oceanian and Malaysia) for the South-East Asian region (Internet 1), while the Dutch had used Insulinde which is equivalent to the Indian Archipelago, while the Anglo-Saxon World used East Indies (Hindia Timur in Malay) and others mentioned earlier. In 1850, Earl in his paper “On the leading characteristics of the Papuan, Australian and Malay-Polenesia nations” in the Journal of The Indian Archipelago and Eastern Asia (JIAEA) vol. IV: 66-70 suggests another names for the Malay Archipelago which he defined before: Malayunesia and Indunesia. This is just a modification of the French “Malasia”, and as a response to other names of this region which contains “Indian” such as Indian Archipelago etc which Earl felt inappropriate. This is the origin of the present name Indonesia.
The French version of “Malasia” had no doubt motivated the Director of “The North Borneo Chartered Company”, Lord Brassey in 1887, to propose the name Malaysia as a new nation for the purpose of uniting all the British territories in the South-East Asia: Sabah, Sarawak, Brunei, Malaya dan Singapura, but it was rejected by the British government 1888 and 1932 (Internet 2). One of the reason would be likely due to the misused of the French word, Malasia. In the same website it is said that the word Malaysian was mentioned in the British North-Borneo Herald July 1, 1929 in an expression Malaysian fauna for a collection of fauna species found in the Brassey’s Malaysia (not the present Malaysia) and presently Indonesia. The Straits Times 13 Sept 1945 have had a head line “Japenese in Malaysia Surrender at Singapore” and the word “Malaysia” here was the English translation/transcription of the French Malasia and Malasien mentioned above.
Of course to other European historians, antropologists and linguisticians, the MW is bigger than those defined by the 19th century British scholars or British colonial administrators mentioned above. To many of these later scholars, MW must also include Madagaskar/Malagasy, Funan-Chenla Kingdom (200-800 A.D) centered in Kampuchea, Champa Kingdom (200-1471) centered in Vietnam, and Taiwan (especially before the formation of the Taiwan Republic of China). The languages of the people in the MW were classified into a single generic name by an Austrian linguistician in the early 20th century and thus unfortunately known as Austronesian instead of Malayanian or Malayonesian. Another official name of the language is the Malayo-Polynesian, but less popular simply due to the towering figure of the inventor of the word Austronesian, namely Schmidt. For the people of the MW, the most common name for the languages is generically named as “Bahasa Rumpun Melayu” (Languages of the Malay World). Most notable languages from the Bahasa Rumpun Melayu (because each has their own numerals and alphabets) are bahasa Melayu (Malay language or simply Malay), Campa, Funan, Jawa, Batak, Bugis, Bali, Sunda, Minankabau and Tagalog. However bahasa Melayu has been also more dominant than others since it has been the lingua-franca of the people in the MW, and also was a diplomatic language at least during the 7th-18th. Bahasa Melayu undergoes three phases of development: the earliest bahasa Melayu known as bahasa Melayu Purba/Kuno (the Ancient Malay) during 78-1300 (especially during Funan-Chenla, Campa and Sriwijaya kingdoms, or simply the pre-Islamic era; the year 78AD is taken in conjuction to the first MW year known as Saka/Syaka); bahasa Melayu Klasik (the Clasical Malay) 1300-1922 and bahasa Melayu Moden (Modern Malay) 1922-now. Bahasa Melayu Purba is also known by the ancient Chinese writers as Kunlun/Koenloen/Kun-Lun/Koen-Loen or Coelan/Kolan by the ancient Greeks (at least since first century). We take the year 1922 as the beginning of the modern Malay in conjuction to the year that the present Romanised/Latinised Malay was used for the first time in the first Malay teaching college, Maktab Perguruan Sultan Idris, MPSI (the Sultan Idris Training College, SITC; now UPSI). It is also very significant year to be noted since it was the year that the youth movement of the Malay World under the Dutch ruled have made a declaration known as the Soempah Pemoeda (the Youth Outh) that the Romanised Malay language will be the official language of their dreamed unified nation-state which would be named as Indonesia.
The characteristic of the Ancient Malay is that her alphabets are from the Southern India known as Palawa/Palawi (Pallava/Pallavi) and many words are from India (mainly Sanskrit, but many also from Pali, Tamil and others). This is the period of Indianisation of the Malay World. The oldest known writing of the ancient Malay dated about 400 AD found in Vietnam (during Campa Kingdom). Before that the Malay expressed their creativity and any form of records and writings in Sanskrit (the oldest record found so far dated 190AD). The Classical Malay is the period of first Islamisation began in the 13th century and the Malay Palawi alphabets slowly been replaced by Jawi (basically Arabic characters) and many Sanskrit words also were replaced by Arabic. The mixture of Malay writings in Palawi and Jawi appear even in the 15th century inscriptions found in Malaysia and Vietnam. The oldest Classical Malay writings is believed to be dated 13th century (some say even 12th century) entitled Bahr al-Lahut (contains cosmology) written during the earliest Pasai Sultanate (now Aceh), although the uncontested earliest manuscripts is the writings of ‘Aqa‘id al-Nasafi dated 1590 (Mahayuddin 2000, al-Attas 1988). The Modern Malay is characterized by the used of Rumi (basically Latin/Roman alphabets) and hence we consider it as started in 1922, as mentioned earlier even though the transcription of Jawi Malay into Rumi Malay was extensively used by the well known a British scholar-colonial-officer in Malaya then, Winstedt 1905 and much earlier by Dutch scholars in Jawa. The earliest known Romanised Malay is a bilingual Dutch and Malay language manusricpt written by Albert Ruil in 1612, and in 1623 Sebastian Dankaerts (another Dutch colonial officer in the Malay World), produced the first comprehensive Latin-script Malay for Europeans. By the formation of Indonesia 1945, the Soempah Pemoeda was vigourously implemented and by 1960’s the Jawi scripts became alient to most Indonesians. Of course Jawi in the British ruled Malay-World was officially replaced by Rumi completely only in 1957 when Malaya achieved her independent whereby Bahasa Melayu Rumi is defined as the official language; that is 12 years after the bigger part of the Malay-World, Indonesia, had already done so. Thus 1957 can be considered as the official year for a complete beginning of a current period of Anglocisation of the MW.
Unfortunately, now we can confidently say that, little is known to the present MW generation with regard her own history of civilization. Thus for example, to the majority of the present Malaysians, Malay civilization is the civilization of an ethnic group in Malaysia, or worse still only the civilization of the Peninsula of Malaysia (earlier, 1945-1962 known as Malaya/Tanah Melayu). With this geographical perception together with the Malaysian constitutional definition of Malay, Malay civilization is considered only from the era of Malaccan Sultanate (Kesultanan Melaka) in the 14th century. Even that, little is known regarding the scientific achievement of an empire with her capitol, “the Eastern Vanice” (namely Melaka/Malacca) as it was referred to by the Europeans at that time) because our scholars were deviated by the colonial masters to study only the Malay manuscripts in arts and literature. At the same time we do not only ignore our pre-Islamic civilization mentioned earlier but also simply forget the other Islamic Malay-World civilizations which attained higher level of scientific achievement, namely Petani Kingdom (1511- 1647), Pasai/Acheh Sultanate (1295-17th century), Johor-Riau Sultanate (16 th century-19th century) and Demak Sultanate (Jawa, 16th -18th century).
Mong scholars, it is only since 1990-an that the situation seems to have changed. Thanks to ASASI who have inspired and motivated a few Malaysia mathematical scientists (notably Osman Bakar and his students at UM, Abdul Razak, Alinor and Shaharir and their students at UKM, and later Mat Rofa and his students at UPM) to study and excavated elements of mathematical sciences in the early MW, although some of them have been doing their work since late 1980’s. In 1992 a group known as Kumpulan Penyelidik Matematik Melayu (Malay Mathematics Research Group) was formed at ATMA, UKM under a bigger group Kumpulan Sains dan Teknologi Melayu, (Malay Science and Technology Group) headed by the Director of ATMA then, Prof. Muhammad Haji Salleh. The group was inactive after ATMA was headed by her new Director a few years later but the group already have discovered a few interesting early MW mathematical sciences which have been reported by Abdul Razak (1997, 2000), Shaharir & Abdul Razak (1998/2001), Abdul Latif (2000), Hanafi (1998), and Hanafi & Shaharir (2000), and Shaharir (1998/2000, 2000) some of which are presented again here below, naturally only briefly. However the research have been continued by the individual members until the author moved to INSPEM, UPM in 2005. In 2005 a research group known as “Kumpulan Penyelidikan Etnomatematik Melayu” (Malay Ethnomathematics Research Group”) headed by the author was formed and her members are almost all of those scholars mentioned above. Later in this paper, for convenience, we refer this research group as KuPeLEMA.
3. The Early Malay World Mathematical Sciences Since the Second Century until Early Islamic Era, the17th Century.
During the last decade of our research we have discovered a few startling findings, some of which have been reported separately by the individual members of the research groups mentioned above from time to time notably since 2000. Contrary to a common belief, during early MW Civilisation, in her Indianised period, 200-1300, notably during what the Chinese writers called the Funan-Chenla Kingdom 200-800 centered at presently known as Kampuchia, the Campa Kingdom 200-1471 centered at presently known as Vietnam, Sriwijaya-Sailendra Kingdom 700-1200 centered at presently known as Palembang (Indonesia) and later at presently known as Pattani (Southern Thailand), and Majapahit Empire 1200-1300 centered at Jawa have excellent development in science and technology, in particular mathematical sciences. The following are some of the major Early MW mathematical sciences which we have discovered:
EM1) Malay number and numerical system (decimal system with zero numeral) had already been invented at least since 6th century A.D., which can be regarded as the oldest in the world (Shaharir 1998/2000, 2001, 2006a & Muhammad Alinor 2006). In particular, we believe that the pre-Islamic Malay word for zero, “sunyi” (inscribed at the wall of the Mehrab in the oldest living mosque in the MW, Masjid Kalijaga, Demak dated 1401S (S=Saka/Syaka, the ancient MW Calendar started 78AD and it has been used until late 18th century) ; from Sanskrit sunya may not be the earliest). Perhaps the Malay word “kosong” is the ancient Malay (Funan-Chenla/Old Khmer) word for zero earlier than “sunyi” as the word in the old Khmer (the Funan Malay) was soh, nd the present Khmer is soan (whereas the corresponding word in Sanksrit, Pali, Tamil or Chinese, the most likely origin of kosong, is morphologically so different). The word “sifar” or for some Malay dialects “sipa” or “sipar” (from Arabic sifr ) naturally appeared in the MW only since 13th century.
EM2) The Malay-World Numerical coefficients which are analogous to those which we are very familiar with namely, mono-/uni-, di-/bi-, tri-, …,deci-, ..and units of whole numbers which are analogous to those which we are even more familiar with such as hundred, thousand, million, billion , trillion… some of them have been used earlier than those invented in the European civilization. For example nano- in Malay is nuka- , duodeci- is is patanga-, whereas laksa (ten thousands), keti (hundred thousands), and wisyilion (10**33, ten followed by 33 zeroes) have no equivalent terminologies in English or even European languages. Although most of the Malay words here can be traced back to Sanskrit but either the meaning have been changed (Malayanised) or more interesting, many also cannot be found in Sanskrit. (Details are in Warkah 2004).
EM3) The terms for Malay numbers are more original than English numbers in the sense that almost all English numbers (e.g below ten) are Anglocised from Arabic (for zero), French, German, Latin, Greek or Sanskrit; but the Malay numbers are all original except satu (from Sanskrit asa) and dua from Sanskrit dwa/dwo/dva/dvo), and perhaps tiga (from Sanskrit tri but some scholars refute this); It is believed that the Malay word for zero, namely kosong, is original and earlier than the word zero (corresponds to the Arabic word, sifr) adopted into English only in the 17th century, even though the etymological study of kosong (zero) is still subject to further as investigation as mentioned in EM1). A comprehensive study so far on the words on Malay numbers (satu, dua, … ) is found in Shaharir & Abdul Razak (1998/2000) and Shaharir (2000). It is interesting to note here for the first time that the terms for Malay numbers morphologically the same as in the Khmer language which shows that both are commonly inherited from the same source namely Funan-Chenla civilization.
EM4) Physical units in MW civilization are abundant and some of them earlier than those invented in European civilization (Shaharir 2006a, Abdul Razak 2000 & Yusharina 2007). For examples saujana (as far as human eyes can see =approximately 0.5 Km; originally from Sanskrit yojana (which is approximately 7.32 Km; originally only used for unit of distances among layers of worlds in Buddhist cosmology), li (approximately 3 meters) and danu (=4 cubits) were units of length since 4th century; sinjol, makik, malau dan satam were units of areas; thil atau tei were units of weights of precious metals such as gold, whereas units of weights for other materials were karsa, dram = 12 thil; pala = 4 karsa, tula = 100 pala dan bhara = 20 tula. As far as units of time are concerned, we have ketika or its original version ghatika or nadika, nimisa (= kelip; about 0.2112 second), kala and nalika : 450 nimisa= 1 kala, 15 kala = 1 ketika (=ghatika= nadika), 40 kala= 1 nalika, and hence 8 ketika = 3 nalika. Thus the stereotyping the Malays as the race who are indifferent toward time; with no precise units of length, area, volume, weight etc. can now be refuted strongly. Even though all of the terminologies for the unit of time are Sanskrit but the Malays had changed their meanings for their own purposes: A Sanskrit unit for time between namisa and kala is purposely left out namely kastha (= 15 namisa; and 30 kastha = 1 kala); and apparently nalika is uniqely Malay unit of time. Similarly with the bigger units of time in Sanskrit, namely muharta (=30.3 kala) and deva-ratri (= day-night=30 muhurta) were not adopted by Malays (a detailed Sanskrit units of time is in Gurudev 2007). The situation is similar to the units of time in the classical Malay: jam (hour) and saat (second). The word jam is originated from Tamil and saat is from Arabic saa‘aht which also means jam but the Malays had changed it into much smaller unit of time than jam (=3600 saat). The word saat must have been adopted by the Malays since at least in the 16th century since the word is found in Hikayat Raja Pasai written in 16th century) but jam must have been adopted very much earlier. The Indonesian Malay detik which means saat must have been introduced in the 20th century after de-Arabisation of the Malay words by Indonesian secular Muslims or non-Muslims intellectuals.
EM5) Axioms for an excellent manager and leader in Malay-World writings were formulated much earlier than those by European scholars. In fact in the MW there is an inscription found in Vietnam dated 1008 AD entitled Cakravantin by an unknown Campa scholar, and another Nagarakartagama dated 1365 written by Prapanca, a renown Majapahit scholar; and the earliest Islamic-Malay-World writings on such topics is found in Hikayat Raja Pasai written by a Pasai scholar in earlier 16th century AD, and more comprehensively in Taj al-Salatin by Bukhari al-Jawhari, a Johor-Riau scholar dated 1603.The earliest writing in this field by European scholar only dated 1525 by Macheavelli in Italian language, whereas the original writing in English was by Leviathan by Hobbes 1651 (details are in Shaharir 2005a,b, 2006a, 2007c, 2006/2007).
EM6) Malay logic during pre-Islamic era of the Malay-World civilization (Muhammad Alinor 2004, 2005a,b,c) and early Islamic era of the Malay-World civilization (Shaharir 2006/2007) are found to be very sophisticated albeit yet to be further studied. For example, influenced by the quranic logical structure in the form of negation and contra-positive are very common. Furthermore the style of refuting a statement is very artistic, as such we may classified the Malay-World refutation as a soft refutation, soft negation or soft contra-positive statement. A preliminary study on the the Malay-World logic during her indianised period has been studied by Mohammad Alinor (2004, 2005). A very comprehensive study on the qualitative nature of Malay-World logic based on perumpamaan Melayu (Malay proverbs) was carried out by Lim (2003) and his findings are uniqely Malay logic which he named it as budistic reason: very fuzzy , which he describes as monolectical (non-dialectical), emotional and yet can be very rational and skillful as shown in the heavy used of budi and hati such as hati budi, budi pekerti, akal budi , hati-hati and many more expression containing “hati”. His findings can be further strengthened by noting the existence of complex relationship between budi and ilmu (sciences/knowledge(s)) in the MW cosmology as discussed in Taj al-Salatin by Bukhari al-Jauhari. This is certainly very challenging for our mathematical scientists in the field of decision science and fuzzy sets in general.
EM7) There were two types of infinities in analogous to the Cantor infinitely countable and infinitely denumerable apparently used at least in early 16th century (Shaharir 2006/2007). Perhaps this can be used to develop our own theory of transfinite numbers.
EM8) Hanafi & Shaharir (2000) find that the popular Malay folk stories are not only rich in MW philosophy of life, but also the MW philosophy of mathematics even though this is subject to further studies.
EM9). The MW cosmology/cosmogony regarding the creation of this universe as described by Nakula and al-Raniri as interpreted by Shaharir (2007b,e) can be further studied to provide an alternative basis for a critical evaluation of the present atheistic cosmology notably that of Hawking.
EM10) The etymological approach of a certain basic word in Malay which correspond to the current mathematical theory such as masa (correspond to time), ruang (correspond to space), urus (correspond to manage), pimpin (correspond to lead) prove to be very useful to critically evaluate the present theory and develop our own theory. This is further elaborated in this paper (Section 4.2.3).
EM11) The high level of mathematical sciences in the early Malay World civilization are reflected in their pioneering works in various technologies. The technologies are in the Champa wats (candis) architecture in the 5th century during the Kingdom of Champa (presently Vietnam), the architecture of the Borobudur Wat (Candi) in the 8th Century in Jawa (one of the wonders of the world) during the Kingdom of Sriwijaya; the ship buildings of the jong (adopted by Chinese as jyanku and later Anglocised as junk), kapal (adopted by Chinese as po, bo, chia-pan and kap-pan) and bahtera since the 2nd century, some specific military technologies (composite materials for making keris, Champa pedangs (swords) and baju besi (armours), Petani’s meriams (cannons) in the 16th century during the Kingdom of Petani (presently south Thailand), and Melaka’s istinggar (a kind of guns) in the 15th century during the Malaccan Sultnates); and the formation of canals, reservoirs and irrigation systems in the 9th century, during Funan-Chenla Malay Civilisation in Kembujadesa (presently Kampuchea); and the presence of a group of chemists known as “orang seri” who were able to produce very potent poisonous chemicals in the 12th century Kingdom of Pasai (presently Aceh). Details are in Shaharir (2006a).
4. The Contemporary Malay World Mathematical Sciences
Every civilization is cyclical and the MW civilization has no exception. The people of the MW have slowly lost their mathematical creativity at least since 18th century, and in fact the Orientalists think that this started when Islam came to the MW! Of course we have yet to be able to strongly refute them. However, since 1970’s it looks as though the MW has experienced a Rennaisance (see Anwar 1996) especially through their Islamic revivalism. Since then, one of the major concerned of some of the scholars in the MW were how to Islamise the western contemporary knowledge, after they have realized that many basic concepts in their own fields were not in accordance or not in harmony with their own system of belief or values. The author believes that almost every member of KuPELEMA precisely experienced that feelings and some of them have managed the stress comfortably and overcome that dilemma by offering new alternative or simply put forward their criticisms on certain aspect of contemporary mathematical sciences and hence hoping for creating more people to become interested in and perhaps be able to give their own contributions as well. The following are some of those alternatives and criticisms.
4.1. Critical Evaluation of Contemporary Knowledge from the World view of the Malay-World
In the last decade also we have shown how our own language, values, religion (Islam), artifacts and culture in general can be used effectively in evaluating the present knowledge in mathematical sciences. This is an important step to produced our own knowledge, a mathematical sciences in our own mould, the Malay-World mould. The followings are examples of such knowledge.
4.1.1 Non-universal Laws of Logic , Sets Theory and Probability.
The non-uniqeness of laws of logic should be conciously realized by all of our present mathematical scientists so that our own laws of logic (as mentioned in section 3) have a proper place in the present mathematical sciences. Logic is one of the intrinsic ways of thinking which are not yet fully understood and the present mathematical logic is just a model of a particular way of reasoning in the Western world. The isomorphism between sets and statements are well known and hence logic and set theory are equivalent. The popular mathematical logic for conjunction, implication etc which are unfortunately abridged as “the truth table” (as if no other way) or become axioms in the Boolean algebra is just a simplest model of logic (refered to as the “hard logic” by the famous creativity theorist, de Bono, through his “lateral thinking” in 1970’s, crisp logic since the invention of fuzzy sets in 1960’s, or simply two-valued logic to differentiate it with the 3-valued logic officially practiced in French legal laws, and a special case for an n-valued logic formulated by Tarski in 1930’s, and the infinite-valued logic in probability). Not just the logic in nano-world (world of atoms), but more importantly, in a cultural setting, is different from that in the “truth table”. A substantial number of mathematical scientists and all diplomats know that different people (race or even ethnic group) have different logical laws (hence sets and probability theories). Most of these phenomena manifestly emerge through their repective languages and others through their actions or decisions which are understood by excellent diplomats and negotiators which are almost all non-mathematicians. Thus, as elaborated in Shaharir (2007a) there are plenty of research to be done in formulating a new mathematical logic and probability and this includes our own logic and probability based on our own language and culture.
4.1.2 A Value Laden Approach to Group Theory and Its Extension
A set of axioms in any algebraic structure is presented in text books in such a away that the subject is not shown as a product of a culture or human values. Axioms of a Group are no exception. This is actually not in accordance with the actual historical development of the subject. For example it is a historical fact that Group Theory was developed in order to solve the problem of roots of a polynomial. It is less known that the theory is also motivated by the problem of “squaring a circle” and “ trisection of an angle”. However none of the course in the Group Theory that we know of were designed to achieve one of this goal. No wonder the course is seen to be useless, non-motivated and non-humanistic to say the least. Of course to change this situation, one needs to study the history and philosophy behind the three problems mentioned above. It is heartening to find out that Abdul Razak (1997) have tried just to do this, albeit not sufficiently enough determination to complete it. He did elaborate the problem of finding roots of a polynomial but failed to connect it to the invention of the axioms of a Group and how the Group Theory solve the problem. Of course we hope Abddul Razak or others will settle this still unresolved problem.
Other historical minded mathematical scientists (especially mathematical physicists) tell us that Group Theory has been developed as an effort to understand the structure of a particular human value, namely beauty: beauty in the atomic structures, and crystal structures. One of the facets of beauty is geometrical in nature known as symmetry (or based on internet dictionary: simetria in Portuguese, symmetrie in Dutch, symetrie in French, samma/prakrama/suvibhakta in Sanskrit, sama in the Old Khmer/Funan-Chenla/Mond, cangkam/cayal/ pativam in Tamil, dui chen xing in Chinese and setangkup/samukur/simetri in the modern Malaysian-Indonesian Malay). It can be shown that the axioms of a Group are exactly the fundamental properties of the geometrical symmetry. The mathematics of symmetry in European Arts, Persian Arts, Indian Arts and “Islamic Arts” have been studied extensively by Western mathematicians not just to match the present theory of their Group Theory but to improve the present theory based on different cultures.What about our own arts? What about our concept of beauty other than this geometrical beauty? Can we characterize it and produce a set of axioms which are different from others? A successful characterisation of the nature of our own arts in relation to the present Group Theory will at least very useful in indigenising the theory and improving our teaching on the subject.
4.1.3. Our Own Theory of Knots?
Knots’ theory is one of the most sophisticated theory in mathematics and proved to be very useful in quantum mechanics, strings and superstrings theory in mathematical physics/physical mathematics. According to Muhammad Alinor (2003), the present theory of knots is developed based on western knots. It is also known that various people have different nature of knots. A discovery of an exotic knot will further extend the present mathematical theory of knots. As a preliminary study for developing our own knots theory, he had compiled a substantial number of Malay-World knots and we believe that he would be able to classify all those knots and hopefully our dream comes true: the Malay-World also can create a history in knot’s theory, or at least can be a basis for teaching the present knots’ theory for achieving greater level of indigenised knowledge.
4.1.4. Critical Evaluation of the Einstein’s Theory and the Quantum Theory
Critical evaluation to the Einstein’s theory from Islamic point of view was first started by the well known Islamic philosopher of the twentieth century, Iqbal (1934/2004) which was translated in (Indonesian) Malay at least twice (1966, 2002). Clearly, his criticism has not been understood or considered deeply by any other Muslim scholars after him until today. Instead Muslims scholars or intellectuals just prefer to take the easier way by accepting the Einstein’s theory and show that it is fully compatible with the Islamic teachings/values as shown by almost every Islamic website, and by apparently widely respected Muslim Indonesian scholar, Wisnu Wardhana (2005) whose book has been reviewed critically by Shaharir (2007d). Others which could as well represented by Maroof Shah & Peerzada (2003) just do not agree at all with Iqbal, partly because Iqbal is not a mathematical physicist or physical mathematician, hence they assume that Iqbal just could not comprehend correctly or maturely the Einstein’s theory.
There have been of course plenty of scholars (almost all of them are non-Muslims) who had criticized the Einstein’s theory from the perspective of mathematical rigour, self-consistency, experimental evidence and her predictive power; and a few of them have been able to produce alternative theories (most of them mentioned in Shaharir 2004b). One of them is presumably a Muslim scholar (a Turkish) named Huseyin Yilmaz (1992, 2005c) and his theory is considered by some as a strong contender of the Eintein’s theory. His main criticism is on the Einstein field equation (Einstein’s gravitational law) which he argues that the equation is incorrect for the case of weak field. Of course many Einstein followers do not agree with Yilmaz and prove that Yilmaz gravitational equation is ill-defined. However for us, Yilmaz does not create a new paradigm at all, in fact his basic axioms on the nature of space-time are the same as in Einstein’s theory. Thus Iqbal criticism is still valid for Yilmaz’s theory as well. In another angle, to our knowledge, Yilmaz had never been interested in the Islamic traditional scholars who had different views on the nature of time and space which are more compatible with the Islamic values and incompatible with the nature of time and space in the Einstein’s theory. Thus, it is understable that Yilmaz simply accepts the Einstein’s theory of space-time and focus only on nonbasic issues of the theory.
Following Iqbal and Whitehead (who had criticised Einstein’s theory ealier than Iqbal but from the Christian-British values) we criticize Einstein’s theory from the Islamic-Malay values (Shaharir 2006c, 2007b). Just as found by Whitehead that the basic terminologies in Einstein’s theory (originally in German) are incompatible with the British values (English and Christian), we found similar situation with respect to Malay and Islam. We further examine the nature of time based on Malay language since his ancient period (ancient Malay) and found that time and space is continuum in a way similar to that which is assumed in the Islamic tradition and the Einstein’s theory but not completely internalized in the theory. We also extend Iqbal discussion regarding the historical and Islamic tradition on the nature of time and space and prove that the nature of time and space in the Einstein’s theory is not fully compatible with our own values. These findings could lead to a new formulation of Relativity Theory of our own.
Another mathematical physics subject which is mathematically highly elegant and sophisticated, and hence very influential in shaping the current Western world view is Quantum mechanics (QM), as it is considered by many as the most successful physical theory ever produced. However QM have been criticized by many since its inception by great physicists and physical mathematicians such as Einstein, Feynman and others (including this author as well) as already presented in Shaharir (2005c). Each of the criticism is based on the incompleteness of the QM, and the physical interpretations of the theory without resorting to any religious values. Instead, religion have been used by popular writers to strengthen QM by showing those aspects of QM which are compatible with the relevant religion. This later position is more prevalent among Muslims, because not a single Muslim scholar had ever criticized QM before us, but instead every Islamic websites and Muslims who have written something on QM, are determine to show the compatability QM with Islam or Sufism. It is as if we have reached at “the end of Islamic knowledge”, i,e no more Muslim who internalized his Islamic values could contribute better knowledge that those in QM. Recently, Shaharir (2004a,b, 2007b) have presented his critcism on QM from an Islamic perspective by elaborating his previous conviction stated in his earlier publications (Shaharir 1990, 2003b, 2004a, 2005c). There he shows that every element of QM which is normally quoted by popular writers as compatible with Islam or Sufism is actually a futile exercise and he shows that the comparison is in fact incorrect. Once again we hope that our Islamic criticism could led to a formulation of a better theory than the present QM as it has been waiting by others, albeit based on different consideration.
The Malay-World also has a rich tradition in cosmology and cosmogeny. Although these fields of knowledge are either based on Hindu-Buddha cosmology-cosmogeny and later on Islamic tradition but they have their own interpretations and hence made their own innovations. We find that in particular the quantum cosmology presented by the famous atheist scholar at the Cambridge University can be criticized not just on Islamic values but based on our own traditional writings, particularly some of the Islamic-Malay principle laid down in the Bustan al-Salatin by al-Raniry in his theory of creation dated in Hijrah which is equivalent to 1639AC. Details are in Shaharir (2007b,e)
4.2. Beyond Critical Evaluation from the the Malay-World Perspectives
During the last decade also we have not only managed to citicise present mathematical theories based on our values but produced a concrete new alternatives based on our mould. A few of such topics are elaborated below.
4.2.1. A Better Concept of Optimum
One of the earliest field of mathematics in which Muslim scholars do realise the Western biasedness is optimization, through the mathematics of utility optimization in mathematical economics. Much earlier realization was contributed by Iqbal (1934/2004) regarding the time and geometry in the Einstein theory, as elaborated earlier. As far as in optimization is concerned , thanks to Kahf (1980), Khan (1984) and Zaman (1987) for criticising the axioms of consumers and hence the axioms of utility function from an Islamic point of view. They have in fact suggested some new axioms which are more Islamic. Their work were later extended and fortified by Shaharir and Rohani (1996) and recently the author focused his criticism on the celebrated Debreu utility theory and propose a new hypothesis of the existence of more Islamic differentiable utility function (Shaharir 2005b). The most challenging issue in the axioms of the utility function (or following Kahf , al-falah function) is to replace the secular concept of commodities (as variables of the utility function) and unsatiablility or greed of the cusumers (both are un-Islamic). For this we have proposed two types of commodities, duniawi commodity and ukhrawi commodity and wustdo (balanced) and arrived at the hypothesis mentioned above. Once this new utility function is settled, we can develop a new theory of utility or consumer behaviour by optimizing the utility function. This is a major programme which should be interested by many especially Muslim scholars
A more general issue in optimization where the author has been emphasized since late 1980-an in his lectures of his optimization courses (undergraduates as well as graduate levels) is the optimization modeling (formulation stage) in which the influenced of culture, philosophy, and values in general are highlighted. In fact, historically optimization problems emerge from an economic consideration, namely the location of a new port (Heron’s problem and believe to be the oldest problem in optimization, albeit a myth), religious philosophy on creation (al-Haitham’s problem on the behaviour of light), Greek philosophy on geometrical forms (Newton’s hydrodynamic problem), the traditional way of making and selling alcohol in European 17th century (Kepler’s problem in optimization on the tradition of his fellow country man in fermentation for making liquor) and others as reported in Shaharir (2002). A similar approach to functional optimization (calculus of variations and functional integration) are also discussed in Shaharir (2002, 2003b, 2004a,b, 2007b) but this is already discussed earlier in section 4.1.4 (on QM). More interesting is in the linear programming modelling where the first problems were in American/Allied military forces during WW2 (determination of the best food for the army and the best number of jetfighters or bombers to be commissioned in a particular combat; details are in Kirby 2003 ).
In general, a specification of an objective function and constraints are both subjective in nature. In fact it was shown in the problem of food for the armies, the technical constraints alone are not enough (armies were not happy with the policy of food provided by the standard naïve mathematical model). The subjective issue such as taste and preferences must be included in the constraints, and hence the subject become very culturally biased. No wonder our scholar, Sutinah (2000, 2001) became very involved in formulating a better linear programming model for fulfilling the need for a particular race, group of people, or even individual. We do not know whether such studies have been done for Malaysians. This would constitute a high grade of mathematics in our own mould. In general, chosing a right objective function is indeed value laden. For example minimizing the cost or maximizing profit is a traditional capitalistic model which is unIslamic as argued by Nik Mohammed Affandy (2002) and Shaharir (2005b), maximizing the level of production is a more compatible with Buddhism or even Islam, although a better Islamic objective function would be optimising the level of iman or taqwa (which is yet to be properly formulated; most likely a vector function). For those who believe in the philosophy of TQM the objective function would be some index for consumers or maximising customers satisfaction which is more Islamic than the maximising profit as an objective function ; for Bentham utilitarianist, it is maximizing the secular utility function, others maximizing nonsecular utility function (such as the Islamic utility function described above); and for a post-modernist it is the optimizing the “return” of some quantity which may not be of his/her liking. The constraints are no less value laden if the model to be more realistic and more acceptable since it must include cultural practice, taste, laws, and other values. Thus it is very meaningful here to be able to produce our own models of optimization (our problems, our culture and our values) as many as possible. (More details are in Shaharir 2005b & 2006b, 2007c).
A more fundamental problem of optimisation in our own mould is to give a new definition of an optimal solution so that it is more compatible to our own concept of “goodness”, “best” , “fairest”, “justice”, “wellbeing”, “sustainable” or “happiness” ; namely those values or virtues which are intrinsic in “mathematical optimization”. We have discussed this in detailed earlier (Shaharir 2005b, 2006a,b, 2007c) and here we would just like to mention only two concepts of optimization namely “optimal policy” for a multiple objectives. We have many (more than ten) concepts of optimal solution, and each of them is value laden and potentialy able to be improved using our own values. Thus optimal solution in the sense of a goal programming is based on a nature of man assumed and articulated by the Noble Laureate, Simon in the 1950’s which he describes man as rationally bounded animal (not fully rational as assumed before) so that man decision is not optimal solution in the sense of the highest or lowest value but instead what he called “satisficing solution” (a new hybrid terminology) and the concept was materialized by Charnes & Cooper in 1970’s via their “goal programming” methodology. We have argued that this is still not quite the same as the best decision based on Islamic principle, namely wustdo. In the above references (in particular Shaharir 2006b), we have obtained a basic theorem on this new definition of optimal solution which we call it optiwus solution. There remains a problem of formulating a new algorithm for obtaining the optiwus solution as effective as the well known algorithm in goal programming problem. Another new concept which we have proposed, albeit not fully developed as much as the optiwus solution, is a modification of the the “efficient solutions”, “dominated solutions” or “Pareto solutions”. We have shown that this concept of Pareto solution is more compatible with elitism and capitalism (liberalism and laissuz-faire economy) and less ummatic as required by Islam. We have modified it to a more ummatic in nature biased and we name it as the optimah solution which is defined as follows: x* is an optimah solution if there is no other x such that for at least hlf of the possible values of i . With this new definition many theorem in the present Pareto optimal have to be modified and hence a new efficient algorithm for obtaining the optimah solution must be obtained.
4.2.2. Islamic-Malay-World Finance Mathematics
Finance mathematics is almost synonymous with the mathematics of interest and this mathematics is one of the most advanced and sophisticated mathematics. Interest or bunga in traditional Malay language is something to be avoided with because it is considered to be riba’ (literally means in excess or increase, and economically in loaned commodity and money usually translated as usury or interest) and hence one of the great sin in Islam. However, Muslims have long faced a dilemma since the formation of banko in the 14th century, the primitive form of the present bank, because apparently this modern version of riba’ does not seems to have an analogous riba’ practices during the Islamic Civilisation and at the same time it is so beneficial and seems to have without alternative. So much so that there have been regarded by many Muslims intellectuals as a dharuraht (a state of emergency) for a long time and then some of them change their opinion to regard it as halal. Only in the middle of the 20th century the ulama’ (wrongly translated by the West, and followed by many Muslims, as the Musim clerics) in the middle East (mainly associated with the al-Azhar University) gave a fatwa (legal Islamic law) on the bank interest: majority of them concluded haram (forbidden/unlawful) and others considered it halal (permissible/lawful). An excellent review on riba’ is in Iqbal (2000?). As a response to this fatwa, Muslims have been unhappy with the conventional banking system. Further response to this situation, an Islamic bank was formed in Egypt in 1970’s which is characterized as “banking without interest”. However nobody bother about the machine behind a banking system, conventional or Islamic, namely the mathematics of interest. They consider mathematics of interest is neutral; only the management of the product from the mathematics is value laden: Islamic or unIslamic. So Islamisation of banking system is nothing to do with mathematics; and of course until lately no mathematician in the world also think otherwise. In Malaysia, as a first response to Islamic revivalism, the conventional financial system, the banks officially change the term bunga into faedah in the 1970’s, but not so in Indonesia (“bunga” is retained until now) partly because Indonesian ulama’ have always been more liberal or Indonesian government is more secularistic and pragmatic.
However in 1980’s, as the wave of Islamisation was high, the government of Malaysia decided to established an Islamic bank and after that it became a history. Indonesia followed suit in 1990’s with the help of Malaysian Islamic bankers. Still the conventional mathematics of interest is the machine for (part and parcel of) the Islamic banking throughout the world; only the terminologies are changed into the Islamic/Arabic terminologies in Islamic business (mu‘amalaht) such as mudharabah, musyarakah, murabahah, mutanaqisah (for replacing the various products on conventional loans/practices for business); profit (untung), dividend (dividen), and services (perkhidmatan) for replacing interest; and the specific products are bay‘in bithamin ‘aajil (for replacing the conventional loan, such as housing loan), Wadi‘ah (for replacing the conventional Saving Account) and various other Islamic/Arabic products, too many to mention it all here. However since the mathematics of interest is implicitly used in the manangement of those new “Islamic products”, there is no fundamental changed in Islamic banking system; or one may say the Islamic bank is still not sufficiently Islamic. In fact a mismanangement of the mathematics of interest together with the principle of Islamic business may lead to a more unjustice to the consumer. This is easily be shown in the bay‘in bithamin ‘aajil whereby a price of a house, for axample, in 20 years time from now is fix and the house is sold to a customer now at that price. This is an example of applying a mathematics from an un-Islamic mould to an Islamic environment! We need our own mathematics.
New finance mathematics with our own mould (Islamic values) has been formulated by a few Malaysian mathematical scholars almost immediately after the establishment of the Bank Islam Malaysia Bhd 1980’s. However the most successful scholar so far is Maheran who work it through for her Ph.D at UKM 2003-2006 under the author’s supervision and toward the end of her research under Abdul Aziz and Zaidi. Maheran and Shaharir (2002,2003,2004) and Maheran et al. (2005,2006) have proposed new mathematical models for financial activities based on mudharabah, musyarakah and mutanaqisah to replace the conventional model based on interest. A new formula for “Islamic loan” (for convenience), for example, is found to be more equitable, just and less burden, as it should be for any Islamic product. A new model of “Islamic option” is proposed which is better than the American or European option found in text books (the Black-Scholes model). However more research have to be done in this area not just to improve the Maheran et al. model for “Islamic option” but to extend Maheran et al. model to a non-Brownian fluctuation, and also to produce a Malay Option based on the traditional practice of Malay jual-janji (Malay promised-selling) which is different from the American and European options. It is also high time for a lecturer who teach finance mathematics or actuarial science not just focuses on mathematics of interest (Western Mathematics) but must also take account some of the mathematics presented here whose details are in Maheran’s thesis (Maheran 2006). To facilitate this implementation, the author would like to suggest that Maheran’s thesis be published.
4.2.3. Our Own History and Theory of Management and Leadership
Based on our finding mentioned in section 3, and many Malay manuscripts (in Jawi) in 16th – 18th century, we can now reformulate, consolidate and develop further our own management science and mathematical political science (theory of leadership as one of its components). We have mentioned it in Shaharir (2005b) and elaborated in Shaharir (2007c) and hence we chose to present it only briefly here.
In Anglo-Saxon management and leadership theory (necessarily in English), it is not uncommon to start the discussion on the theory by studying the etymology of “manage” and “lead” and obtain some basic principle of management and leadership axioms from it. Thus, we have done an analogous investigation on our own language, and that is to study the word “urus” and “pimpin” (Shaharir 2005b, 2006a, 2007c). We found that unlike the the corresponding English words, the two words are original Malay-group words and they have shades of different meaning from the corresponding English words. Once again we have reached at a definite example whereby a language has a role in creation new knowledge (earlier in this paper we have shown in Probability and Relativity Theories). We thus have proposed a meaning and a relationship of a pengurus (manager) and pemimpin (leader) in our own mould and described their relationship even mathematically: a manager is a limit point of a leader.
Further, we have found two pre-Islamic Malay-group management-leadership theory as mentioned in section 3, EM8). We have studied extensively the theory in Cakravantin based on the axiomatic method (in mathematics) as the method becomes a respected method in the Western management science as shown by Kirkeby (2002). We found that a type of manager-leader implicit in the Cakravantin is a person with 5 virtues/values. Details are in Shaharir (2005a). Further studies should be in order to obtain separate axioms for manager and leaders only based on virtues since Kirkeby have shown virtues are more fundamental than values. We have yet to study a newer management-leadership theory based on 18 excellent behaviours of manager-leader in Nagarakartagama of Prapanca. One should be able to extract simpler and precise axioms of excellent managers and leaders from these manuscripts. However some works toward this goal are found in Shaharir (2005b, 2006a, 2007c).
When Islam was adopted by the people of MW, a new development in their management-leadership theory emerges. We have found the oldest Islamic Malay Management-leadership theory is in Hikayat Raja Pasai by an anknown writer (dated early 16th century), followed by in Sulalaht al-Salatin/Sejarah Melayu by Tun Sri Lanang in 1612, Taj al-Salatin by Bukhari al-Jauhari in1603 and Bustan al-Salatin by Nur al-Din al-Raniri in1638. We have obtained three sets of axioms of excellent leaders from the three manuscripts, and two sets of excellent managers from the last two manuscripts. Axioms of excellent leaders in the Hikayat Raja Pasai are a mixture of feudalistic Cakravantin and Khalifah which may be contradictory; whereas in al-Jauhari and al-Raniri they are still traces of feudalistic Cakravantin but dominantly Islamic. Details are found in Shaharir (2006a, 2006/2007, 2007c) .
It is interesting to note that not all writings in management-leadership by the well known scholars during Islamic Civilisation and later became well known in Europe reached in the MW (until recently). For example the writings by al-Farabi and Ibn Sina have not been found in Malay-World manuscripts, and in fact present traditional Islamic MW scholars do not seems to refer to their writings as shown by the best seller book on Islamic Malay-World leadership by Andek Masnah (1999/2001). Andek Masnah is perhaps the only writer that we know of who have used the axiomatic method in analysing the work of a group of scholars during the Islamic civilization which includes al-Ghazali but excluding those names mentioned above and presented a set of axioms of excellent leaders. However the axioms not only seems to be not independent but also contains an unacceptable axiom regarding the decendent of a leader, and less comprehensive than the axioms which have obtained through our scholar, al-Jauhari mentioned above. Details are in Shaharir (2006a, 2007c)
Regarding the present writings on the Islamic management-leadership (since the Islamic revivalism 1970’s), we find that almost all of the Malay World writers have not been working in the Malay-World mould which has been developed since the Cakravantin era for about a millennium ago, or since the Hikayat Raja Pasai in 16th century. They are either at the early stage of indigenistion (translation of the work Islamic scholars during the Islamic Civilisation) or too absorbed to the Islamisation of the Western management-leadership theories at the expense of Islamising their own heritage of knowledge (such as Cakravantin and Nagarakartagama) or improving or extending their own Islamic heritage such as Taj al-Salatin and Bustan al-Salatin. In Shaharir (2006a, 2007c), this state of affairs is elaborated and a methological research programme for further development of our own theory of management-leadership based on our rich resources is proposed. Thus it is heartening to know that Ong (2004) have managed to publish a management theory of our own based on Hang Tuah and commercializing it successfully; but it is sad to know that our scholars are still following the West to study SunTzu such as Kho (1990) and Aidit (1997/98), even though Sun Tzu (500SM/1986) has been partly indigenized since his manuscript had been translated into Malaysian Malay 1986 and Indonesian Malay much earlier. Still, we should have more Ongs among us.
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