Comparative Knowledge of Mathematics and History

In our society today, the application and value of shared or personal knowledge have proven to greatly alter the value of that knowledge. Within this essay, I will be comparing the application of knowledge within the AOK of mathematics and History. Knowledge can be defined as knowing that is anything based on facts or opinions or anything that can be said to be either true or not true. The AOK of history can be described as recounting the events of the past, and the AOK of mathematics can be described as “the branch of science concerned with the number, quantity, and space, either as abstract ideas (pure mathematics) or as applied to physics, engineering, and other subjects (applied mathematics)”.

When applying that knowledge within the AOK of mathematics and History we can discuss that knowledge can be pure or applied, shared or personal. Pure knowledge can be described as the knowledge that will benefit you indirectly and in the long run, whereas applied knowledge benefits you directly and immediately and is obtained from our senses.

We could also discuss this claim through shared and personal knowledge. Where shared knowledge is a shared context that is denotative and personal knowledge usually refers to a conative aspect. When looking into these classified aspects of knowledge, we can conclude that the application that they have in the real world is of value. For example, through this knowledge individuals can communicate with each other. Therefore we can question, to what extent is the dependence of the value of knowledge applicable to the real world?

The value of shared knowledge is of greater value than personal knowledge within history.

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The application of history can be studied through the WOK lenses of language, reasoning, and intuition. One perspective within the AOK of history is by looking at history through a cyclical lens. Where the patterns involved in history could be viewed as cycles where, by looking at History, the application of this knowledge would serve as predictive power. Before I go into this, I will first discuss what makes history. In the textbook given to us by the IB that for something to become evidence of history it needs to be looked at to argue for an interpretation of the past. Therefore, certain reports can be looked at as evidence of history. An overall overlook of history is progress, the development from the caveman threshold to today’s society. Historical events in a line of progress, and applying that history we could project where we are heading o. This can be supported through the lens of language as a WOK. Historians can use language as a major means for eyewitnesses to give us their knowledge. Through the use of language humans and promptly historians have benefited greatly from using communication, understanding, and interpretations of each other. Intuition also plays a role as within history there is no definite answer and have to make predictions based on past information which could be subjective, leading to imperfect and sometimes inaccurate predictions as those predictions are based on subjective knowledge. Historians can review pieces of history through collective knowledge and communicate that knowledge amongst other individuals. This can also be interpreted as shared knowledge.

Which is a shared context is essentially denotative. To the IB textbook “shared knowledge changes and evolves because of the continued applications of the methods of inquiry—all those processes covered by the knowledge framework. Applying the methodology belonging to an area of knowledge has the effect of changing what we know” (IB). This refers back to my argument about cyclical history, where objective notions of measures of success go to predicted notions of history. Historians use patterns, language, and reasoning, to able to predict future history, through linguistic analysis. For example, the publicity surrounding the atomic bomb of Hiroshima and Nagasaki in 1945 assured the American government in the Cuban missile crisis of 1962 to advertise a nuclear holocaust, due to the spread of images and horror stories surrounding the 1945 bombing. The shared knowledge that is directly applied to the real world is of great value. History is inevitably applied with frequency in the world, making it an area of complete relevance. If one’s view is that history is cyclical, history repeats itself but historians need to learn from mistakes and understand one’s past, as well as the past of others otherwise history wouldn’t have the same impact. Therefore accounting for that shared knowledge is of great value as it brings us closer to certainty.

However personal knowledge does have an impact on history making it of value. Personal knowledge could be described as knowledge referring to a more conative aspect of knowledge. This can be seen when studying the event of 1972 when there was a break-in at the Democratic National Committee where Richard Nixon’s administration attempted to cover up the involvement as did the president himself. This led to the constitutional crisis in the US. Had Nixon shared his knowledge with the public instead of withholding it, the outcome would have been completely different. thus, personal knowledge can hold value within history. Individuals can obtain personal knowledge by looking into a plethora of WOK, as one’s perspective on that knowledge can differ in terms of behavior, emotion, and reasoning. One can also argue that the application of one’s knowledge aspects, refers back to how perspectives differ from one another. In my RLS, withholding personal knowledge could also be argued that one is withholding the application of knowledge. Therefore, as one is withholding the application into the world, the value of knowledge is reduced as it reduces certainty, but as personal knowledge and the acts of both revealing and withholding information can alter our history it irrefutably has value as a result.

In the AOK of mathematics, the applications of pure and applied mathematics can be studied through the WOK and lenses of Language, imagination, and reasoning. First I will distinguish between the two areas of mathematics. Pure mathematics would dive into the realm of ideals, attempts to discover theories and relationships, and do math just for doing math. Whereas applied mathematics is maths with practical use, where those theories and relationships are applied to models that model, predict, and explain things in the real world. Pure mathematics also is not concerned with the direct practical applications to the real world and labor, while applied mathematics does. Relating to the central claim of this essay, we can discuss that there is a difference in the values of knowledge between applied and pure mathematics.

If we look at the number theory relating to pure maths, on its own the theory is not able to be applied to the real world, therefore diminishing its value in the promotion of education and wealth. Pure maths can be described as separate from the physical world. “It solves problems, finds facts, and answers questions that don’t depend on the world around us, but on the rules of mathematics itself. They simply stay has theories of knowledge with no applicable use within the world. Whereas, applied mathematics, more specifically engineering, is applied throughout the world. Such as fluid mechanisms that analyze how fluids are affected by forces. Other examples include architecture and statistics or probability theory. Although there are distinctions between pure and applied mathematics, they both hold value as there is rigorous proof to back it up.

However, as usual in the classification between two abstracts, some distinctions between pure and applied mathematics seem to be incorrect. It is described that the establishment of applied mathematics resulted from successful applications of pure mathematics to real-world problems. Through the WOK of language and reasoning mathematicians were able to share their knowledge within the area of study to come up with practical methods that can be applied to the real world. An example of this is Albert Einstein’s theory of relativity sets forth the equation E=mc2, where (energy equals mass multiplied by the speed of sound squared) This theory was mainly used within ‘the Manhattan Project. Einstein used the Lorenz transformations to his ideas and deduced his theory of relativism. Another example that I will discuss, is the Pythagorean theorem discovered by the famous Greek philosopher Pythagoras. The Pythagorean Theorem states that: ‘The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.’

This theory was then applied to real-world situations through applied mathematics and is now the foundation for geometry and trigonometry, which can be used within the practice or architecture and the accuracy and liability of map-making. Being able to apply it to real-world scenarios, has raised the value of knowledge as it has provided us with new development and technology, most famously the GPS, mobile devices, safe air travel, etc. But let’s say he didn’t share his knowledge with the rest of the world. Would we still be where we are today, or would his knowledge affect the course of history? Pythagoras also used the WOK of sense perception, reasoning, and imagination to come up with his theory. And by sharing his knowledge amongst other mathematicians, his theory underwent a process of peer review through the WOK of language as mathematical symbolism is a subset of ideas developed in language, where peers examine each other’s work to make it more reliable by eliminating error. Mathematicians can build upon each other’s ideas as maths is completely abstract and can lead to new conclusions that were not readily apparent. This raises the value of that knowledge.

Conclusion: To answer my knowledge question, I think that the value of knowledge is dependent to a great extent on the applications within the real world in both areas of AOK in History and Mathematics. Within history, the considerations of shared and personal knowledge can greatly alter the value of knowledge as it impacts the outcome and the predictability of history looked at through the lens of WOK of language and reasoning. Shared knowledge can highlight certain future outcomes discussed with the nuclear missile bombing, whereas personal knowledge could withdraw certain information that could affect certain events or outcomes. In the AOK of mathematics, the distinction between pure and applied mathematics differs in value as pure mathematics can not always be applied to the real world, compared to applied mathematics which constantly is applied to the real world. However, there are imprecisions and inaccuracies within the classification of the distinction between pure and applied mathematics that the very establishment of applied mathematics results from the field of pure mathematics and applying that to real-world scenarios. I discussed this through Einstein’s theory of relativism and the Pythagoras theory where the AOKs of imagination, sense perception, and reasoning create new-found knowledge, and langue ensures that that new knowledge is maintained and spread to preserve or build upon that new-found knowledge.