Category: Science

Perspectives on Mathematics

 – Kanhaiya Jha
Students often feel that what they are taught is useless in practical life. French Philosopher  and  mathematician Rene Discartes (1596 – 1650) once said, “People hate maths, so let’s turn it into picture to make it easier.” Often, the student does not easily understand what is being taught because he is unable to visualize what in fact is going on. But it is the only subject where one may get hundred out of hundred, yet people say it is difficult. It definitely requires more effort and time than other subjects. But due to its wide applications and importance, it has been made a compulsory subject worldwide for the students in the school level to university level curriculum and more weightage have been given to maths. As knowledge of English language helps people to communicate well with others, maths has been proved to have the same role as science and technology. Therefore, to understand the existing technological developments, maths has become a necessary tool. But one does not need to be a mathematician; one at least requires knowing about the widespread contribution of mathematics. 
Maths is the base for almost all scientific developments and modern technology.  Maths is also used as a powerful means of communication. An updated Standard syllabus and equivalent recognized text books of many universities help students to develop an understanding of theoretical concepts as well as problem solving skills in maths. Teachers can play a vital role for motivating students towards this  subject, giving more applications and connecting it to other fields. Knowledge is unlimited, so a healthy and regular interaction between teachers and students can produce beautiful results. Students can derive more benefit from studying maths only when they appreciate its beauty and operate it properly. Topics with elementary roots and strong interconnections should be taught with great care. Instead of making straight leap to the problems while at the classroom, some preliminary discussion on how, when and why particular concept developed helps to create a positive attitude.
Definitions in maths ensure that everyone agrees on the meaning of the terminologies and concepts. Theorems in mathematics provide the user with the reassurance of validation and a model of logical argument. The use of theorems and logical arguments lead the mathematicians to only one correct (exact) solution. By doing maths, students develop skills in problem solving, reasoning, connections and communications. The skill developed by doing maths makes students efficient, accurate and confident decision makers. However, it is possible only when they appreciate its intensity and work hard. It requires regular practice and more concentration on the topic. Not only can this broaden our horizons, but also provide an opportunity to apply our knowledge and skills in the applications of mathematical sciences to other fields. Also, modern mathematics education emphasizes the development of understanding among students. Maths continues to flourish through the growing power of its applications and much of its utility is enhanced through the computer. Indian and Chinese mathematical systems have been highly appreciated by the world mathematicians and due to their remarkable achievements and significant contributions, they have been able to establish themselves as top in software technology. Today, the mathematician works in a world of intense scientific investigation aided by a revolution in methods of computation and means of communication. His thinking is a part of the whole climate of intellectual thought in which distinction between the pure and applied, abstract and practical is too subtle to be of much use.
Maths is a fascinating world – a world full of mysteries and wonders, a world full of joy and excitement, of divine beauty and grace. No other area of human activity is ever as glamorous as maths and yet is depressing. It should be kept in mind that the study of maths is never complete unless one can apply what one has learned in solving problems of real life and in intellectual gymnastics.

Science and Pseudoscience

– Pushpa Raj Adhikary
Natural philosophy in early days was the study to find unanswered questions about nature. The equivalent of natural philosophy now is science. As the answers about the nature were found, these gradually became part of what is now called science. We, now, know that science is divided into various branches of study, namely, the study of living beings known as biology, botany, zoology, genetics, molecular biology, and physical science known as physics, chemistry, geology, meteorology and astronomy.
Biology is more complex than physics and chemistry because it involves not only matters but living matters.  But in some schools biology is taught before physics and chemistry because biology consists  mainly of classifying plants and animals. Scientifically, biology is much more complicated than physics and chemistry . But almost all the high school students consider biology far easier than the most fundamental of all sciences, the physics.
Where does mathematics fit into this picture of science? Is mathematics a branch of science? Of course, mathematics is a branch of science with its well established foundations and very powerful methods of studying mathematical objects. Mathematics can also be regarded as art because creativity of highest order can be displayed in mathematics. Mathematics is also a language of science. We want to express scientific ideas as precisely as possible and in unambiguous language. Ordinary language will not help scientists to express their ideas correctly. For example, consider the following expression,
2 / [3 + ( 5 / 3 ) x 6 – 2 + 3 ( 6 + 8 ) / 3 { 5 – 9 / 3 + 2 } x 5 ]
If you try to write down the instructions as how to simplify this expression in plain language, it will create more confusion than clarity. But for those who understand the meanings of symbols involved in the expression, it is quite clear how to simplify it. Mathematical language is very clear and offers an unambiguous way of expressing scientific ideas mainly in physics. So, sound knowledge of mathematics is required to study science.
As in ordinary language, scientific language also uses the term ‘facts’, ‘hypothesis’, ‘law’, ‘theory’, ‘concept’ and ‘prediction’. These terms often mean different in science. A fact means something absolute in ordinary language but in science facts evolve. People do understand that the meaning of hypothesis is speculation. But for a scientist, it is an educated guess about nature or model of nature that seems to explain its laws. Hypothesis and theory may  seem to mean the same in ordinary language but in science a theory is an accumulation of ideas and equations of well -tested hypothesis and laws.
A law in science describes how nature behaves. A law of nature is a statement expressing what has been seen always to happen in certain conditions. A law is a scientific principle. The principle which governs how a stone falls to the ground from the height is the law of falling bodies. Newton’s law of motion  explains the motion of bodies on earth and also the movement of celestial bodies.
A scientific theory is a reasonable or scientifically acceptable explanation for a fact or event, which may not have been proved to be true. A scientific theory consists of rules or principles, theorems, etc. belonging to the subject. For example, set theory deals with the behavior of groups of mathematical elements known as sets. A useful theory in science is able to predict how nature behaves in connection with some unknown phenomenon, or how things or events may turn out in some specific conditions.
The explanation for a fact or event made by a scientific theory is tested for its validity by experiment(s). A hypothesis explained by a scientific theory and confirmed by an experiment becomes a scientific principle or law.
Often, we speak of scientific method of learning. Scientists make discoveries by this method. The work of Galileo in the sixteenth century established the scientific method of gaining, organizing, and applying new knowledge. A scientific problem generally recognizes a problem, thereby making an educated guess or hypothesis for the cause of the problem. Then we predict the consequences of the hypothesis and perform experiments to test the validity of our predictions. Based on hypothesis, prediction, and outcomes of the experiment, we formulate a principle or a rule. But great discoveries made by scientists not always follow these rules. Often these discoveries were made by trial and error or accidental cases.
A hypothesis in science must be testable. The chance that a hypothesis can be proved wrong is also as likely as it can be proved right. A scientist accepts the wrongness of a hypothesis as easily as he/she accepts its correctness. Actually instead of asking “Am I right?” scientists want to know “Why am I not wrong?” The emphasis on finding the wrongness in all cases distinguishes science from non-science. If there isn’t a test to determine whether a hypothesis is wrong or not, it cannot be a scientific hypothesis.
Consider, for example, that the planets affect our destiny. Neither we can prove that it does,  nor  have we proof that it does not. Till we can prove or disprove it, it cannot be a scientific hypothesis. In the same way, whether there is the existence of god or whether god created this world cannot be proved or disproved. Thus, such subjects are not within the realm of science and there are no scientific answers to such questions.
Theories of science are not fixed. They undergo change. When our understanding of our surroundings or nature increases, accordingly the theories of science also become more and more perfect.  Newton’s law of gravitation helped us to understand the motion of planets, and based on this law, humankind could land on moon, but it cannot explain the formation of black holes. So, we need more perfect theory of gravitation to explain what happens in a black hole than that of Newton’s. The more we understand about nature,  the more perfect theory of science will be.
Science does not subjugate nature, but goes along with natural laws. But we know of some acts that try to subjugate or force nature to act in some strange ways, by some kind of magic or so-called supernatural powers. Even with the advancement of 21st century science, we are still unable to dispel the so-called magic which persists in societies, beginning from the primitive to modern day societies. Such ‘magic’ which does not stand to be tested for right or wrong is pseudoscience. We talk of mysticism but quite a few may even believe it  to be nothing but pseudoscience. Likewise, astrology, which is considered science by its practitioners, is also a pseudoscience. The practitioners of pseudoscience are misguiding the society. Occasionally such practitioners do get success and are able to fool people but their success is nothing but mere coincidence. We have come a long way in comprehending nature and liberating ourselves from ignorance but, still, it is not sufficient to free ourselves from performing some mystic experiments for more wealth and power, to believe in astrology and occult phenomenon. Daily newspapers hardly report on the progress of science and new discoveries, but never forget to publish a column of horoscope. So, more human effort is required to fight against this inclination for pseudoscience.

Perspectives of Mathematics

Kanhaiya Jha
Distinguished scientist and former Indian president Dr. A.P.J. Abdul Kalam summarizes the significance of science to the mankind thus: “Science, more science and still more science is needed to lay the foundations for the development and growth of an individual, a society, a nation and world.” Science has made invaluable contributions in the progress of different civilizations of the world. Math-e-matics has been defined as the science of numbers and the structure and measurement of shapes, including algebra, geometry and arithmetic. It is Ganita which means the science of calculation. Mathematics is a vast system of organized thinking of an analytic and synthetic nature developed since the golden ages of Greece and the earlier Babylonian civilization. Mathematics in ancient India was one of the most advanced and practical sciences amongst all the early civilizations of the world. Ancient Indian mathematicians were popular because they had a clear concept of numerical quantities with nine digits and a zero. Indian mathematicians have always given remarkable contributions to the world mathematics. The great Indian mathematicians like Aryabhatta (5th century AD), Bhaskara (12th century AD), Brahmagupta and Chinese mathematicians like Sun-Tsu, Lin Hui, Wang H’siao-T’ung, Ch’in Chiu-Shao made various discoveries, which were unknown to the rest of the world, during the same period. There are evidences of some connection between Greek mathematics and Indian mathematics and of an intimate connection between Indian mathematics and Chinese mathematics. Nepalese mathematicians like Gopal Pande, Nay Raj Pant have also made some contributions in the history of Nepalese mathematics. 
Mathematics, as an expression of human mind, reflects the active will, the contemplative reason and desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generally and individually. The term “mathematics (maths)” has been interpreted and explained in various ways. It is the facts and relationships between them. It explains that this science is a bi-product of our empirical knowledge. That is why famous mathematician Karl Friedrich Gauss (1777-1855) defined maths as the “Queen of Science”. Much of the same sentiment is expressed in an ancient Sanskrit verses: 
“Yatha Sikha Mayuranaam, Naganam Manayo Yatha/
Thatha Vedanga Shastranam, Ganitham Murdhani Sthitham //”
This means: “Like the combs of the peacocks, and the crest jewels of the serpents, the love of jyotisa (Ganita or computation) stands as the head of all the loves forming the auxiliaries of the Vedas.”
Almost all results in maths are developed through the process of reasoning (inductive as well as deductive). Now, some familiarity with maths has been regarded as an indispensable part of the intellectual equipment of every cultured person. Regarding the role of maths, famous English biologist Charles Darwin (1809-1882) wrote: “Every new body of discovery is mathematical in form, because there is no other guidance we can have.”
Mathematics as a whole can be divided into three main branches, each of which has its own history: (i) geometry, astronomy and chronology; (ii) algebra and (iii) analysis. Clearly, it is found that these three branches often overlap. Also, modern maths has been classified into pure and applied mathematics. Pure maths deals with the fundamental concepts and is abstract in nature. Applied maths is the application of continuous forms of maths (calculus) as an insight into or solution for “real word” problems. Applied maths reflects the belief that basic order and harmony exist in the physical words, which may be described by the logical structures of maths. Famous mathematician P.R Halmous has said: “Applied maths cannot get along without pure, as an anteater cannot get along without ants, but not necessarily the reverse.” Whenever we try to compare maths with the other branches of science, then due to its exactness, maths always dominates the other sciences. Since each experiment or research work carries some sorts of calculations, other branches cannot be independent of maths. Till the present day, maths has helped to develop different fields. In order to solve a real life problem, we need the interaction between physical, mathematical & life sciences in a meaningful way. Life sciences present many challenging problems for physical and mathematical sciences. In connection with physical sciences, maths has been used in physics, chemistry, biology and engineering; and in connection with social sciences, it has been used in economics, statistics, psychology, logic and fine arts in many forms.
A mathematical system is an abstract deductive theory that can be applied in other mathematical situations when the axioms can be verified. The success of application in other fields of knowledge depends on how well the mathematical system describes the situation at hand. Also the power of maths rests on the discovery that it was possible to represent abstract concepts such as those of numbers and shape by means of concrete symbols; and through the physical arrangement of these symbols with respect to each other to express relations between these concepts. Thus, permissible rules for the changing of the arrangement of the symbols reflected permissible steps in expressing logical relations between the original concepts.
Everywhere in the world, maths is considered to be a difficult subject. If we search the Internet using the keyword ‘hate’, mathematics is likely to be the term most associated with the term. Now maths is one of the subjects you cannot simply ignore. As Glenn Mason-Richeborough pointed out, “Maths is important from the view of the individual as well as of the society.” Maths is the most objective among all the sciences, yet the act of realizing maths in our world creates subjectivity. We all respond differently while learning it. These facts reveal that the real fault lies not in maths but in the way the subject is taught. Both teaching and learning maths have been greatly influenced by the recent development in Information Technology. But the ancient mathematical approaches provide us the best techniques in our understanding of maths. That’s why school students in many developed countries are still afraid of solving decimal problems with hands. In maths interest is relatively difficult to sustain in comparison to other subjects. A problem may be solved in a number of ways. Once the students understand the fundamentals, the actual solving becomes a simple task. And once students start getting answers right, confidence builds up and mathematics becomes more of fun. Certainly everybody cannot learn maths except only a meager part of it. Unless one is endowed with certain qualities, one cannot learn maths. The qualities are (i) Mental alertness (ii) Venturesomeness (iii) Tenacity and (iv) Diligence.
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[To be continued in the upcoming issue]

Science and Superstition: Reflections on Astrology

Pushpa Raj Adhikary
One area where science and superstition clash and confuse is astrology.  The clash and confusion stem from a popular misconception that astrology is the same scientific field as astronomy. In this article I will try to shed lights on the different facets of this misconception. 
In fact, the same ancient people, who made sense of the worldly things, also observed the sky, calculated the positions of prominent stars and planets and other heavenly bodies with respect to the earth and acquired the knowledge, which could predict the occurrences of solar and linear eclipses. Thus emerged the knowledge of astrology which mainly dealt with predicting the impacts of the positions of the sun, moon, planets, and stars on the events which occur on earth and the future lives of living beings.
Do the position of stars and planets in the sky, at the time of birth of a child affect the future of the child’s life and career? Astrology says it does. But how? The systematic and formulated knowledge accumulated so far does not have a rational reason to correlate a position of a certain planet or a star with that of life and career of any person. If so, then why and how does this strange belief of correlating the stars and planets with our future exist in our society? This belief persists in our society because of the curiosity of human beings to know whether some natural phenomenon brings about the well-being of particular person or persons. The astrologers come with their explanation to convince us that the position of a planet or the position of the sun in a particular constellation (rashi) at the time of their birth does affect the destiny of the new born. As a proof of their claim they asked: if astrology is not true or not a science, how can an astrologer predict the phenomenon of eclipse?
Of course, people wanted to know and also record the time of the birth of their children. Without a clock or the calendar how would people do it? The most obvious way of doing this was to record the time with respect to the position of the sun in a particular group of stars, which we call rashi, or the position of a planet, or a star. We have these positions recorded in a paper called the ‘horoscope’ or kundali. An astrologer reads time recorded in kundali and predicts the future of a person. Now a days, with such a large population on earth, it is most likely that several persons may be born at a particular time of the day. But do you have any record of such persons born at a particular time having identical habits, attitudes, or career? During the time of the election two different astrologers predict different outcomes for the same candidate. Is this not the proof that an astrologer’s prediction is a wild guess but not the outcome based on rational thinking?
Let us now briefly discuss about the subject called astronomy. Astronomers also observe the sky, record the position of planets and stars. They not only record the positions of the planets and stars, but also try to understand how stars and planets move in the sky, why they look different at different times of the year. Astronomers also study why stars are different from the planets, why stars are hot, how stars are formed, how long the stars survive, and most importantly, where all of these stars, planets, comets and other bodies in the sky come from. Does any book on astrology explain or answer any of these questions? Astronomy is a science and it keeps growing once we understand more and more of nature’s secret. But do you have the similar expansion of knowledge in astrology except something about the position of planets and stars and their impact on human beings? A branch of knowledge which does not improve continuously but becomes more and more perfect, and above all, satisfies the intellectual quest of human beings is not a science and is also irrelevant to us. And astrology is one of such branches of knowledge whereas astronomy, since its beginning to the present time, is equally interesting, challenging and requires greatest intellectual power of human beings to understand the material bodies and their interactions resulting in the form of natural phenomena.  
Our ancestors who studied sky and tried to understand the planet, stars, and their motion in sky did not necessarily do so to link their knowledge in predicting the future of human beings on earth. They studied the sky as part of human curiosity to understand about their surroundings and satisfy the intellectual quest. But somehow this knowledge, instead of growing as a science has grown to a pseudo-science misleading the society. These days astrologers not only tell you about your future but they predict whether you go abroad or not. Astrologers have even started to make a horoscope of a country. Would we, as rationale beings of a new millennium, like to be the citizens of a country whose fate is decided by astrologers?
Astrologers try to influence us in almost all of our activities including the area of our economy by predicting the rise and fall of stock market. They have even fooled politicians by making them more prone to astrological consultations. But how often do the predictions of astrologers come true? Have you had any record of how many predictions of astrologers have come true? The belief in astrology is thus based on a motive for a quick gain without any hard work. In fact, we should start taking astrologers to task for making false predictions which would affect the life of many.
It is true that science does not have answers to the many unknown phenomena in our lives. The efforts of scientists are directed to understanding the reasons for observing the objects around us  which are not explained through the existing knowledge. But astrologers may have answers to many questions which science does not have because they would not need reasons and logic to answer these questions. They put blame on some unknown planet or star and try to convince us this particular star or planet has determined our action or future. If you are a rationale human being you would not believe anything of it and discard this as total nonsense and regard astrology not as a science but superstition.

Science and Superstitions

 – Pushpa Raj Adhikary

The English dictionary describes science as systematic and formulated knowledge. Let us explain more elaborately the meaning of science. In the beginning of human history, humans were like wild animals. Slowly and bit by bit they started learning about their surroundings. Such learning was necessary for early human beings for their food and safety. The learning of one generation was passed on to another generation. Instead of parents transferring what information they had to their children, it was thought better to combine all information or knowledge of all parents and pass on to the next generation. The combined knowledge kept by a group of people or a tribe has come to be known as the culture. The factor necessary for the advancement of culture is communication, which includes speaking, writing, and various forms of arts. Communication helped to interact among different cultures and what is passed on by this communication is history. Thus history is the study of cultures.

Where does science fit into this picture? Science is only one of the important parts of our culture. The combined knowledge through generations to generations which helped human beings to survive, prosper, and be on the top of the development is what we mean by systematic and formulated knowledge.

Ancient human beings lived in the fear of darkness. They were susceptible to diseases, insects, hurricanes, floods, earthquakes, cold, and heat. All these things were nature’s threats to living beings. Early human beings could not understand why and how such miseries did occur. Somehow they thought someone who is very superior to them is creating such miseries to them. They attributed one superior being for each of their miseries and thus created gods of hurricane, water, rain, cloud, flood, cold, heat and so on. They believed the causes of their sufferings were the results of the unhappiness of one or more of these gods, and constantly tried to please the gods to avoid the miseries and sufferings. Due to the lack of power to reason they cultivated a senseless or irrational fear of the unknown or the mysterious. Such fear is described as superstition or irrational religious system.

We have to examine how science and superstitions affect our daily life and our thinking. We have a long cultural tradition where religion plays an important role. Our puranas and other religious books have a large number of stories and incidents describing miracles performed by saints and gods. These stories conflict with our rational minds and our scientific understanding of our day to day life with nature. Do you believe that the eclipses are caused by the demons Rahu and Ketu? Do you believe that your destiny is decided by some heavenly body or bodies situated at million of miles away? Many of us have a habit of depending on the horoscope as a way to know the future. The position of a planet or a star at the time of your birth does not determine your destiny or future. What shapes your future is your attitude towards life and hard work but not the heavenly bodies made either of cold hard rocks or very hot gases. There are many stories about the unknown phenomena. Rather than believing in such stories and in irrational explanations one should try to understand these unknown phenomena on scientific basis.

Superstition is the irrational way of explaining usual or unusual events. Science does not believe in irrational way of explaining events. Science aims to know the cause and effect of each phenomenon based on scientific principles that can be verified with experiments and are proven on the basis of well-established scientific rules known as laws. Science has rational answers to many of the phenomena.

No scientist, however great he/she is, ever claims that he/she knows everything. A scientist always says, “I do not know” instead of making an irrational explanation of an event. But the fact that there exists no proven scientific answer to any of the nature’s secret does not mean that the answer is known to a religious pundit, or it is written in some saastra, or it is said by some saint or god. Scientists are continuously trying to understand why and how events take place until a rational answer is found. That we have not yet understood many secrets of nature does not mean that god has forbidden us to know those things or we are inferior to god, or we can never understand all the secrets of creation.

Conflict between science, superstition, and religion is not unique only to our culture but in the western society too. The church opposed the idea of Nicholas Copernicus who said that the earth is not the centre of the universe, a belief which was accepted by the Bible. Several other scientists had to suffer the wrath of the church for their scientific beliefs which contradicted with the Bible. But their ideas ultimately got accepted and helped to end the superstitious belief of the religion. In his book The Grand Design, Stephen Hawking, one of the great scientists of our time, says that philosophy has not kept up with modern developments in science. Scientists have become the bearers of the torch of discovery in our quest for knowledge.

 

 

 

Biotechnology: Boon to Humans

– Dhurva Gauchan
The science of biotechnology is an amalgamation of biological sciences and technology. Biotechnology is the youngest of the sciences and is increasing in knowledge at an unprecedented rate. It is the fastest growing technical discipline and has probably gained more information per year than any other field of science. Advances in biotechnology even outpace new developments in computer science. Because of the rapid advance, biotechnology is called a revolutionary science that literally challenges the ability of people to keep up with an understanding of applications in society. In 21st century, no one can anticipate better life without the use of biotechnology because of its versatile applications in all the branches of science. 
There is always a big question why biotechnology is popular  among the advanced biological sciences in the world. It is popular because of its broad spectrum application which encompasses the day to day requirements of human race such as agriculture, dairy, forestry, pharmaceutical, fermentation, environment and medical science. Its interdisciplinary nature makes  it more acceptable by the scientists and ordinary men as well. 
The global population, which numbered approximately 1.6 billion in 1900, has surged to more than 6 billion and is expected to reach 10 billion by 2030. There is an estimation that world food production will have to double on existing farmland if it is to keep pace with the anticipated population growth. Biotechnology can help meet the ever-increasing need by increasing yields, decreasing crop inputs such as water and fertilizer, and providing pest control methods that are more compatible with the environment. 
Biotechnology has immense scope in agriculture, dairy industries, medical and health care in Nepal, especially in crop improvement that could be a great contribution for the inhabitants of the outlying areas. Nepal is exponentially rich in natural resources and biodiversity. Its flora and fauna has great potential to serve the humanity. 
Our country faces problems regarding biotech expertise and all the necessary facilities needed for carrying out quality research works. Nepali scientists from home and overseas can do collaborative industry-based research projects. Lucrative government policies can attract the international biotechnology companies/ donor agencies for investment. We are very rich in natural resources but our labor is inexpensive.

I may dream in daylight but I could not leave the hope to draw the very lavish picture of establishment of biotechnology in Nepal. We can drag the success and make our dream come true if we get the brain gain. Well trained Nepali scientists from all over the world must yoke in the same platform for the noble cause. Private companies and government of Nepal collectively put their collective efforts to pave the way for the upliftment of Biotechnology. Industrialists from Nepal should take sincere interests to fund  the innovative ideas of scientists for production of biotech products.

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