The most striking evidence that mathematics and natural sciences share such common associations is in, for example, the scientific field of physics. By simple definition, physics is the practical application of mathematics in the real world. Thus, it is clear that these two areas of knowledge are not clearly separated but are interdependent. However, we realise that our physics lessons are different to our maths lessons because of the content, and the practical way in which we learn.
History and the human sciences, also called the social sciences, are other examples of areas of knowledge that share common links. The social sciences concentrate on the study of human behaviour, human society and social relationships. History is documented human sciences of the past. Similarities posses these areas of knowledge, and consequently separating these can be difficult. History can be thought of as the gathering of facts from the past, but the way we view these facts can be perceived differently, according to our ethical beliefs. For instance, the dropping of the atomic bomb on Japan can be viewed differently depending on one’s values. Does the killing of 240 000 Japanese outweigh the advantage of bringing World War Two to a halt? While history may rely on research and empirical evidence, we are also forced to make decisions about what is right and wrong. This makes it almost impossible to separate ethical knowledge from the human sciences.
Indeed, ethical concerns inter disperse all areas of knowledge. Ethical choices often need to be made, for example in the case of stem cell research in biology. Some believe it is morally right to further research in this area, as it can greatly help or cure people who are sick, injured or disabled. On the other hand, some believe that it is wrong to exploit and destroy that which could potentially be a person (as stem cell research requires the removal of stem cells from an embryo, destroying the embryo in the process). Mathematics and natural sciences are not always objective, nor is any other area of knowledge. We must consider ethical implications of our actions in all fields of research, even those based on reason and logic, because these rules govern our way of life.
Natural science is invaluable in the pursuit of historical fact. Forensic science uses specialist techniques in crime detection to recreate history using the scientific method. This means we cannot disregard science when studying history, because so much of what we know about history is discovered through the natural sciences.
Although mathematics and the human sciences are different areas of knowledge, they are closely linked. In economics for example, economists are constantly looking for a trend of why the stock market behaves the way it does. They look for mathematical relationships, so they can predict the outcome of stock in the future. Similarly, geography looks at the studies of human population. A popular graph in understanding people is the demographic transition model. This is as a result of research conducted of other individuals, and formulated into a general graph, for easy interpretation. However, these two areas of knowledge can be in contrast to each other. Humans are an unpredictable species, and for this reason mathematical principles cannot be applied. While numbers remain constant (4 will always equal 4), humans are constantly changing with new experiences. So, while often demographics can help us understand societies, it is very difficult to make predictions about human behaviour, let alone from a mathematical theorem. Natural sciences and mathematics do contribute to our understanding of the world and us, but the unpredictability of human behaviour means we cannot use logic and reason exclusively.
A further area of knowledge is the arts, which comprises of a huge range of human creativity. The arts are very much subjective, and contrary to the sciences, the arts are based primarily on emotion. Because of this, often the way we express our emotions and ideas is artistically. Concepts in the sciences, for instance, are often expressed through art, a good example being the work of Leonardo da Vinci. He studied the human body, physics and created artistic masterpieces simultaneously, because he realised that both the arts and sciences are studies of the world around us, using a different medium. This is another example where it is hard to differentiate areas of knowledge, as they are inextricably intertwined in each other. The arts encompass every area of knowledge in our life, and there is no easy way to make a distinction.
A further example in arts, mathematics can be used. In the past, a golden ratio has been used to portray emotion in paintings. Fibonacci’s sequence is a number pattern as a result of the addition of the previous two numbers, e.g. 1, 1, 2, 3, 5, 8, and so on. The golden ratio uses this to its advantage; a bigger number divided by the number that goes before it to give a constant. This is approximately 1.618. Paintings drawn in a frame of 1 proportional to 1.618 are, for whatever reason, the most appealing to the human eye. This provides an interesting link between artistic ‘appreciation’
and patterns in the natural world. This shows how knowledge issues cannot be easily classified, because often they overlap. Although creativity is the mode for expression in the arts, any area of knowledge can have creativity.
So what practical reasons underpin our division of the areas of knowledge? Knowledge is so vast, and in order to study in depth a topic, we must specialise. For example, at a year 12 level, an IB English teacher could never teach IB Physics unless he/she had studied physics. Also, libraries use the Dewey Decimal System to organise their collection of easy retrieval. Universities also classify knowledge into distinct areas: science and the arts. The depth of knowledge one learns at university level makes it essential to break down areas of knowledge into specialised subjects, due to the vastness of knowledge. However, the broader Areas of Knowledge classifications, such as the Natural Sciences, allow for diverse subjects such as astronomy and marine biology under the same heading, focusing on their similarities rather than their differences. I think that therefore they are flexible enough for our purposes in our education.
To conclude, the areas of knowledge must be divided for practical purposes, but nonetheless are all interlinked. However, we know, when studying that they are distinct, albeit with similarities in our approach to learning. Although all areas rely on each other, we have found a way to separate these areas, mainly for convenience. Thus, the classifications dividing the areas of knowledge are not always justified; they are a division by humans to make education and knowledge, amongst other things, more manageable.
WORKS CITED
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POMPERAUG HIGH SCHOOL “Were there Other Possible Solutions?” The Atomic Bomb () (3 Jul 2002)
WOOLMAN, M. (2000) Ways of Knowing Victoria : IBID Press
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LITTLE, J. Book Review of Mathematics and the Loss of Certainty by Morris Kline
LITTLE, J. Book Review of Mathematics and the Loss of Certainty by Morris Kline
GIANCOLI, D. (1998) Physics New Jersey, USA : Prentice Hall
ZIEMKE, E. “World War ll”, Microsoft Encarta. (CD-ROM) 1996 Microsoft Corporation
MAASSEN, V. “Fibonnaci’s Sequence and the Golden ratio” Fibonacci Patterns () (3 Jul 2002)
WOOLMAN, M. (2000) Ways of Knowing Victoria : IBID Press