6. Magic

6. Magic

Question 6: “In knowledge there is always a trade-off between accuracy and simplicity.” Evaluate this statement in relation to two areas of knowledge.
1. Maths
  1. Accuracy
    1. Mathematical knowledge, if proven based on deductive logic and using the axioms and postulates that are defined as true, is always accurate. The deductive logic means that every step is supported completely, and so no inaccuracies will result. However, what is worth exploring is the accuracy of which maths is able to depict reality. Does the maths conform with reality? Are the mathematical predictions accurate? And finally, how does the simplicity of maths affect how accurate it is of a representation of reality. In essence, something is accurate in maths if is a good representation of reality
  2. Simplicity
    1. Simplicity in maths is when the ideas are easy to follow, and understandable. The more the ideas are understandable, the simpler they are. For example, the Rieman Zeta function uses complex notation that the majority of the world will not understand, and so it is not simple. However, the sum 1+3=4 is easily understood by most people in the world. Even though not everyone can understand it, it is still simple in the sense that it i easy to understand.
  3. KC1 - Accuracy of the statement is not affected by the simplicity of the language
    1. mathematical notation, universally agreed upon symbols, one interpretation
      1. Not dependent on language used in maths
        Only dependent on logic and reasoning
    2. Ex. Area of triangle
      1. Half ab sin c
        Same Answer Ultimately
      2. Half bh
  4. CC1: simple mathematical models are not enough to be an accurate representation of reality
    1. Simplification sacrifices accuracy
      1. Ex weather forecasting, cubes of air of atmosphere, patterns of airflow between the cubes. Greatly simplified because model can be complicated by considering more cubes and/or making the cubes smaller.
2. Natural Science
  1. Accuracy
    1. Similar to maths, knowledge in the NS is accurate when it is a good representative of reality. It is only accurate if it can predict or describe reality as it is, Even though our sensory perception may limit us, we can still maximize the accuracy by using tools. Thing is, the essay isn't about accuracy in itself, but the trade-off between accuracy and simplicity.
  2. Simplicity
    1. Knowledge is simple in the natural sciences when it can be easily understood and learnt by people. There are some types of knowledge in the natural science which can be explained using both simple and complex terms. For example, quantum mechanics can be explained simply using common words in any particular language. However, it can also be explained using mathematical language that is difficult for most people to understand as it brings in complex mathematical concepts. The point is to evaluate whether this detracts the accuracy of that knowledge or not.
  3. KC2: When using language to explain the concepts, the simpler the language used, the more inaccurate it is. For example, we can explain thermodynamics using both simple language and complex mathematical notation. When using simple language, we can summarize the laws into "you can't win", "you can't tie" and "you can't get out of the game". This is easy to understand, however, we lose vital information, as it does not show how exactly each of these conclusions are obtained, and the relationship between variables, for example, mathematically the second law of thermodynamics states ????. We see that it displays a lot more information than the simple statement "you can't tie", and so is a more accurate representation of reality as it includes more factors than the simple statement.
    1. Use of language
  4. CC2: Occam's Razor, the simplest explanation is the correct one. When forming conclusions from eperiments, typically, the simpler the explanation, the more accurate it is. This is because if we overcomplicate the conclusions that we may obtain, there are many assuptions inherent that may not be directly proven, therefore the knowledge is not accurate.
    1. Actual theory
      1. Different types of simplicity; simplicity in language, and simplicity in the actual theory
  5. AOK
3. Introduction
  1. Define
    1. Accuracy
      1. The quality or state of being correct (Oxford Dictionary)
        Correct: Representation of Reality
    2. Simplicity
      1. the quality of being easy to understand (Oxford Dictionary)
  2. Knowledge
    1. Introduction
    2. RLS
    3. KQ
      1. TWE does the simplicity impact on the accuracy of the knowledge conveyed in the AOKs of Maths and Natural Science
      2. AOK
      3. WOK
        langugage
  3. Final Verdict
    1. See conc
4. Conclusion
  1. Sum of the Claims
  2. Linking to Original Question
    1. There is never ALWAYS a trade off between accuracy and simplicity
  3. So What
    1. If there is no trade-off, we should maximise both the simplicity and accuracy possible, in order to make the best decisions and to make calculations easiest, therefore gaining the most utility out of the least work, or resources
5. If there is always a trade-off, should we prefer accuracy over simplicity?
  1. Find a balance?

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	Created by Alan Lai over 8 years ago