TOK Essay. The entire accuracies of mathematics and the natural sciences rely on the four ways of knowing.

by ozzie95 (student)

International Baccalaureate Theory of Knowledge

Ousainou Corr

TOK 1

Exercise 4

The Areas of Knowledge

May 18th, 2012

Our understanding of the natural sciences is lengthened through descriptions and explanations. The natural sciences consist of biology, chemistry, and physics. We need to describe and demonstrate these sciences in order to be able to understand them. Yet, they also can serve as explanations themselves for other topics. Yet, we still need to be cautious about the claims that are made in the natural sciences as they usually are not the complete truth. For example, when the atom was first observed, the information was not complete and partly incorrect compared to what we have today. But, maybe in the far future, our beliefs about the atom today would be countered with the rapid advance of technology. So, just like other areas of knowledge, the natural sciences also have their weaknesses and limitations. But they can serve as explanations for other topics. In comparison, mathematics is another area of knowledge that can be described and explained meaningfully in order to explain other areas of knowledge. Yet, the natural sciences and mathematics differ in their methods of explanations and how they are described.

The entire accuracies of mathematics and the natural sciences rely on the four ways of knowing. Actually, the natural sciences rely on all four i.e. language, perception, reasoning, and emotion, whilst mathematics only requires three of the four i.e. language, perception, and reasoning. In the natural sciences, language is an important aspect of it. In order for two scientists to be able to converse, they must have equal understanding on a topic. They must understand the terms used. For example, a biologist cannot talk to a chemist about enzymes. A biologist will be talking about how enzymes, such pepsin in your saliva, help with digestion to speed it up. Yet, a chemist will talk about how enzymes speed up chemical reactions. Ideally, they will be talking about the same things, but their terminology will be different and cause miscommunications and there might be lack of understanding between the scientists. So language is a necessity in the natural sciences. For perception, the natural sciences require you to use your senses almost always. In chemistry, biology, and physics, you need your eyes to observe your experiments. You may also need to touch, for example in chemistry, to see if a reaction is endothermic or exothermic. Tasting is the one thing that is not required in any of these sciences, as lab equipment and substances used in the lab are not safe to be out in one’s mouth. They are highly dangerous and can lead to complications and even death. Smell is also another sense that is used. You can smell when something is burning or when a reaction is occurring. Sometimes, reactions let out odors to let you know when they are occurring. Reasoning is necessary as you need be able to, with the background knowledge you have, be able to draw conclusion from reactions. For example, if you see that a reaction released heat, you should be able to reason and draw the conclusion that it is an exothermic reaction. Emotion is another way of knowing that is used in the natural sciences. When writing a hypothesis or prediction, it is your own decision, based on how you feel about the experiment, to guess on a result. Your feelings are also your emotions, and each person’s opinion or feeling about an experiment is different from anybody else’s. In mathematics, only three of the four ways of knowing are required i.e. language, perception, and reasoning. Language is needed as two mathematicians should be able to converse about an equation or question without having to explain everything due to confusions. The ‘math language’ should be common between the two conversation holders. Perception is important as you need to understand how an answer is reached and also understand how to solve and use certain equations or formulae. Reasoning is important as you need to be able to look at a question and the answer and see if the answer is reasonable. You need to be able to reason and see the possibilities and incorrect answers. This is how these two areas of knowledge may be established with the ways of knowing.

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Theory is something that can mean many different things in many areas of knowledge. In the natural sciences, a theory does not just seem to be knowledge. It is something that is not justified as it may change. It is more of supposition than anything. It is something that, maybe, when looked into in the future with greater technology, may seem to be false and a greater answer could be provided. For example, the theory of evolution could be altered in the future if the evolutionary patterns seem different and less reliable as they are today. In mathematics, however, a theory is knowledge. It is justified true belief. We are supplied with formulae and other keys that help us solve for answer. But there is only one possible answer or set of answers. It is something we KNOW. It cannot be altered in the future. There may be alternatives, and they may even replace our current strategies, but our current strategies will still be justified, just old fashion. The idea does not change. It is just presented in another manner.

In the natural sciences, we usually describe the ideas of the sciences with experimentation. With experimentation however, at times, we are not sure about our results. We can only hypothesize. We test the claims in order to understand how the claims were arrived at and also understand how we can alterations to reach other findings. For example, in chemistry, in order to observe and understand enthalpy changes, we do a specific heat capacity experiment. We also understand aspects that cause faults in the experiment so we understand how uncertain our results are. For example, heat can be lost to the environment. So we put our hot water in a Styrofoam calorimeter so that we do not lose any heat to the environment and so that we can have results as accurate as possible. Another example is that, in biology, in order to understand DNA, how each individual’s DNA is different from anyone else, and this can be used to solve crimes, we practiced gel electrolysis, in which we put our different samples of DNA in wells in a gel square and run an electrical current over the gel in a solution. As a result, we get bands in the gel of different thicknesses and frequencies, so we can differentiate between the samples. At a crime scene, if a DNA sample is found, like blood, it can be compared to samples from suspects to find the criminal and punish him accordingly. In physics, we can prove how the force of an object will be the product of the mass and the acceleration of an object. For example, if we are given, numerically, the mass and acceleration of car hitting a tree, we can find the force. But if we do not trust our answer, we can test our claim using a car of the same mass and accelerate at the same acceleration given. This is how you can test this claim. So basically, the natural sciences can be proven by experimentation. In mathematics, we use rational and logical relationships to understand this topic. In math, there are not multiple possible solutions. For example, 2 + 2 cannot sum up to any other value. The answer will always be 4. And this is proven to be logical using real-life relationships. For example, a question could be “If Michael had 2 apples, and John gave him 2 more, how many apples does Michael have now?” and the answer would be 4. In all mathematics, you would use the four functions (+, -, x,÷). Even in the most complex higher level mathematics questions, there is still at least one of the four functions. In mathematics, we are always trying to prove a mathematics problem. So it seems that, in mathematics, the only way we can explain mathematics is with, well, mathematics. As a matter of fact, one could even go to say that mathematics IS an explanation on its own, especially when it comes to the natural sciences. In chemistry, most of stoichiometry is calculations using math and the four functions. For example, converting a mole value to grams would require you to multiply the mole value by the molar mass of the element. In biology, we do averages of values to find an average value of, for example, plants germinated. This also requires mathematics. In physics, almost everything requires mathematics. A good example is the car example previously mentioned. You need to multiply the mass by the acceleration to find the force. So, mathematics seems to be more of a method of description on its own, describing other areas of knowledge, such as the natural sciences. But the natural sciences are mainly described using experimentation. This is not really a comparison in this case, but rather one area of knowledge, mathematics, contributing to another, the natural sciences.