Not too long later, I learned in additional mathematics, certain trigonometric identities of the form cos(A ± B) = –(cos A cos B ± sin A sin B), from which we can form another identity: cos A cos B = ½ [cos(A + B) + cos(A – B)].

This identity is the basis of an obsolete technique known as prosthaphaeretic multiplication, which is very similar but older than the log-antilog procedure taught by my teacher. To illustrate prosthaphaeretic multiplication on 10.8 x 87.85, we proceeds as follows: First write 10.8 x 87.85 as 0.108 x 0.8785 x 10000, then read the arccosine values for 0.108 and 0.8785 from table, they are 1.463 and 0.498 in radians. With the identity, multiplication of two cosines is converted to addition/subtraction of their respective arccosines, that is,

10.8 x 87.85 = cos 1.463 x cos 0.498 x 10000 = ½[cos(1.463 + 0.498) + cos(1.463 - 0.498)] x 10000

The result is 945, which is very close to the exact solution: 948.78.

At the time, I thought, the only sensible reason for retaining the log-antilog procedure in a modern mathematics textbook in the year when we were building the Petronas Twin Towers was that the syllabus designers want us to appreciate the hardship and tortuous path gone through by astronomers and arithmeticians a few centuries ago when they need to multiply numbers.

However, if they want us to fully appreciate how mathematics is done a few centuries ago; they should put the prosthaphaeresis in the textbook. The real reason, as I now believe, is because the syllabus designers are insensitive to technological environment which is ever changing. One or two decades ago, when electronic calculators became cheap and popular, they should have reformed the curriculum and remove the obsolete techniques like the log-antilog procedure.

Luckily, our syllabus designers have now changed their minds. The modern math syllabus was reformed a few years ago and the log-antilog technique for performing multiplication is now removed. However, the harm cannot be undone, as we students could have spent our time more productively a decade ago.

## Thursday, February 28, 2008

## Monday, February 11, 2008

### Professor Nik Hassan Shuhaimi Nik Abdul Rahman: Part I

I came across a rather harsh commentary by Prof. Wilhelm G. Solheim II on a recent JMBRAS article written by Prof. Nik Hassan Shuhaimi, to which Prof. Nik replied bitterly in seven points.

Therefore, I decided to run a quick biographical check on both Prof Nik and Prof. Solheim.

Nik Hassan Shuhaimi Nik Abdul Rahman is currently the president of the Association Malaysian Archeologists. Academically, he is with the Institute of the Malay World and Civilization in Universiti Kebangsaan Malaysia (UKM).

Prof. Nik was born February 4, 1944. He received his early education in Malay School Kubang Keranji, Kota Bharu and the famous Malay College Kuala Kangsar. Between 1962 and 1963, he went to study in Technical College, Kuala Lumpur. In 1965, he was admitted to the Malayan Teachers College in Penang. After obtaining his teaching certificate, he returned to Kelantan and taught in Kubang Kerian Secondary School for about 4 years.

After the riot in May 1969, he was admitted to the University of Malaya to study history. 4 years later, he obtained his B.A. degree, at the age of 29.

After graduation, Prof. Nik applied to become a tutor in the Departments of History, UKM and his alma mater. Before he was called to UKM, he taught briefly (about half a year) in Sungai Besar.

In 1972, Prof. Nik was fortunate enough to be selected by the UKM Academic Staff Training Programme. The result was his enrollment in the prestigous School of Oriental and African Studies (SOAS), London. Prof. Nik spent approximately 48 months there doing his doctoral works on Indo-Malayan Buddhist sculptures.

Unfortunately, it is highly possible that Prof. Nik was unsuccessful at his first attempt in getting himself a PhD degree and awarded a MPhil instead. His MPhil Thesis is "Buddhist sculpture from Sumatra, Peninsular Malaysia and Peninsular Thailand during the Sriui Jayan Period (7th-14th century A.D.)".

When he returned to Malaysia in 1976, Prof. Nik was immediately appointed as a lecturer in the Department of History, UKM.

Four and a half years later, UKM sent Prof. Nik to SOAS London for a second time. This time, Prof Nik chosed a slightly different topic: Art, archaeology and the early Kingdoms in the Malay Peninsula and Sumatra: circa 400-1400 A.D. After about 40 months of research works in SOAS, Prof. Nik, at the age of 41, was awarded his PhD degree.

Shortly after Prof. Nik completed his doctoral degree in 1984, he was promoted to Associate Professor and was chosen to head the Department of History, UKM. 10 years later, he was promoted to full professor in 1993.

Therefore, I decided to run a quick biographical check on both Prof Nik and Prof. Solheim.

Nik Hassan Shuhaimi Nik Abdul Rahman is currently the president of the Association Malaysian Archeologists. Academically, he is with the Institute of the Malay World and Civilization in Universiti Kebangsaan Malaysia (UKM).

Prof. Nik was born February 4, 1944. He received his early education in Malay School Kubang Keranji, Kota Bharu and the famous Malay College Kuala Kangsar. Between 1962 and 1963, he went to study in Technical College, Kuala Lumpur. In 1965, he was admitted to the Malayan Teachers College in Penang. After obtaining his teaching certificate, he returned to Kelantan and taught in Kubang Kerian Secondary School for about 4 years.

After the riot in May 1969, he was admitted to the University of Malaya to study history. 4 years later, he obtained his B.A. degree, at the age of 29.

After graduation, Prof. Nik applied to become a tutor in the Departments of History, UKM and his alma mater. Before he was called to UKM, he taught briefly (about half a year) in Sungai Besar.

In 1972, Prof. Nik was fortunate enough to be selected by the UKM Academic Staff Training Programme. The result was his enrollment in the prestigous School of Oriental and African Studies (SOAS), London. Prof. Nik spent approximately 48 months there doing his doctoral works on Indo-Malayan Buddhist sculptures.

Unfortunately, it is highly possible that Prof. Nik was unsuccessful at his first attempt in getting himself a PhD degree and awarded a MPhil instead. His MPhil Thesis is "Buddhist sculpture from Sumatra, Peninsular Malaysia and Peninsular Thailand during the Sriui Jayan Period (7th-14th century A.D.)".

When he returned to Malaysia in 1976, Prof. Nik was immediately appointed as a lecturer in the Department of History, UKM.

Four and a half years later, UKM sent Prof. Nik to SOAS London for a second time. This time, Prof Nik chosed a slightly different topic: Art, archaeology and the early Kingdoms in the Malay Peninsula and Sumatra: circa 400-1400 A.D. After about 40 months of research works in SOAS, Prof. Nik, at the age of 41, was awarded his PhD degree.

Shortly after Prof. Nik completed his doctoral degree in 1984, he was promoted to Associate Professor and was chosen to head the Department of History, UKM. 10 years later, he was promoted to full professor in 1993.

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