History is the study of the past. Mathematics is the study of concepts such as quantity, structure, space and change. Therefore, since the two areas of knowledge differ, the acquisition of knowledge in these areas will also differ. For example, the methods used to gather historical information/data cannot be used in mathematics: one will not try and find historical objects as archaeologists do in order to acquire knowledge in mathematics because the result has no link to the knowledge area of mathematics. It is therefore clear that acquiring knowledge in the knowledge area of history will be different from acquiring knowledge in mathematics. The Ways of Knowing (language, reason, emotion, perception) are instrumental aspects in trying to acquire information in any Area of Knowledge.
The way that these Ways of Knowing to affect the acquisition of knowledge in the different Areas of Knowledge varies because the methods for acquiring data in the knowledge areas vary. This difference is particularly noticeable in the acquisition of knowledge in history and mathematics. This essay will investigate how the Ways of Knowing to affect the acquisition of knowledge in both history and mathematics and in what ways history is more affected than mathematics. This difference will lie in the variation between what history is concerned with and what math involves. Studying the past always involves reference to primary and secondary sources used to prove the existence of certain events and information.
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Sometimes, historical information can be proven wrong as it is inaccurate based on the events that actually occurred. But mathematics involves a more systematic approach because there is only one right answer and it is very easy to prove whether one is right or wrong. Knowledge in mathematics can be justified by the use of proofs, which are constructed by mathematicians through logical reasoning. Although proofs can be obtained in history, some are subjective as they could be based on primary sources such as an interview with a person who was involved in a certain event in the past, and others are difficult to obtain because they occurred in the past.
History has a link with the Ways of Knowing which cannot be ignored because it is very evident. Firstly, exploring emotion, the people in the past had certain feelings because they expressed joy, sorrow, anger as well as fear. These emotions can have multiple meanings because they were manipulated and interpreted by historians. The way that historians have manipulated these emotions has affected the importance of certain events in human history. For example, a famous historian Huizinga said that “people in the Middle Ages are wild, cruel, prone to violent outbreaks and abandoned to the joy of the moment” (The Perception of History as a Science). The actions of the people of the Middle Ages could have been determined by their emotions and the way the historians have interpreted this information has had a significant impact on the importance of certain events in the Middle Ages.
Language in history can be explored through Beowulf, part of old English literature. Beowulf was composed in an Anglic dialect, at a time when the English spoken today did not exist. Those who spoke English in those times never claimed that the Anglic dialect was a version of the Standard English spoken today and hence it was a huge shame for them because they could not interpret their own language. In addition, the interpretation of Beowulf was done differently when composed in the Anglic dialect and when translated to Standard English, showing that history can be interpreted differently based on the language that was used then. Reason in history is mainly explored through why certain events occurred. However, along with perception, the real account of events and emotions experienced cannot be accounted for because even some primary sources can be subjective or biased as they could be written from someone’s perspective and hence this brings uncertainty to the existence of certain historical events that have not been proven through logical reasoning.
Mathematics also has a considerable link with the Ways of Knowing. Firstly, I am going to observe the link between mathematics and emotion. Emotion is largely linked to mathematics because of the feelings involved with mathematicians or problem-solvers when acquiring mathematical knowledge. For example, a personal experience is that I have experienced joy and delight at solving a problem and hence acquiring mathematical knowledge. Such an experience can only change the approach one has to acquire mathematical knowledge when solving a problem again. Mathematics can also produce heated arguments in a discussion of mathematical concepts. In addition, continuous work with mathematical problems can develop a sense of familiarity with the problem-solver as there are patterns that the problem-solver is able to notice.
Since there is intellectual cognition involved when observing patterns, this is an emotional quality. Although mathematicians do not discuss it most and mathematics is seen as an unemotional acquisition of knowledge, there is a certain level of emotion involved. Language in mathematics mainly takes the form of symbols that are used in order to represent certain functions. Mason, a great researcher, said that “words generate more words in explanation, but often draw us away from the experiences from which they stem” (Worrying about emotions in history). Referring to this, Mason largely bases his link of mathematics and language on the reflection of the experience of acquiring mathematical knowledge. Mason states the mathematical experience can often be misinterpreted which means that language is a major barrier in the reflection of experiences.
Mathematics holds a certain truth and it is upon the problem-solver to find it. The way that the problem-solver interprets the symbols in Mathematics is seen as an interpretation of language and is often a barrier for the problem-solver trying to seek the truth. The influence of perception on mathematics is mainly in the way that the problem-solver interprets mathematical data through the use of sight. Since there is only one way to interpret a mathematical problem, perception has a minimal impact on the acquisition of mathematical knowledge. However, perception has a link with language in that if the problem-solver does not understand the symbols for functions, they will not be able to solve the problem and hence acquire knowledge. Reason in mathematics is slightly ambiguous because it is difficult to explore why certain things occur in mathematics. Mathematics involves a systematic approach and involves logical reasoning because it is just logic for things to happen the way they do.
In addition, this logic can be proved by mathematicians, once again using logic so reason does not influence mathematics because it is rarely the case where problem-solvers ask why things occur the way they do in mathematics. The aim of this essay is to explore the apparent greater link of history to the Ways of Knowing than mathematics. Based on the information presented above, it is clear that there is a certain difference in the effect of the Ways of Knowing on history and mathematics. In terms of emotion, history is affected greater than mathematics because the feelings that people in the past experienced is much more important to the significance of certain events in historical context than the feelings mathematicians experience when solving certain problems. The feelings that people in the past experienced can determine why certain historical events happened while problem-solvers are only interested in the way to solve the problem rather than the feelings of the mathematicians in mathematics.
In terms of language, I believe it is more important in history because some concepts can be misinterpreted or even ignored when analyzing old literature or historical events because of the change of language. In mathematics, language is the representation of symbols that can only take one form. For example, an addition symbol can only mean to add because there are no other ways of saying to add in mathematics while in history, certain aspects can be lost when translating from old languages into the new dialects used today. In terms of perception, I also believe that history is effect more than mathematics. The five senses come into account during the real event and therefore when analyzing historical events in the present, the actual situation can be misinterpreted because of the lack of sources/ logical proof. In addition, sources can be biased as they as subjective and hence historical interpretations cannot be based on them. In mathematics, perception is only needed through sight, in order to interpret the problem, which can only be interpreted in one way as the mathematical symbols only have one representation.
In terms of reason, history once again is more affected because, in mathematics, proofs can be developed to outline why certain aspects occur the way they do. However, it is often difficult to outline why certain historical events occurred because of the lack of information. In addition, the other Ways of Knowing also play their part when looking at one Way of Knowing ex. when analyzing perception, the sense of hearing can be affected through the use of language at that time in history. In conclusion, the effects of the Ways of Knowing on history and mathematics have been analyzed. I have concluded that history is affected more because it is more subjective, while mathematics is based on logical reasoning. History is affected more in all the four Ways of Knowing because mathematics is very systematic and has one firm representation in its language while history can have several, making it more difficult to interpret.
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