Q6 | Mind Map

Extraction
1. Importance/Introduction
  1. Knowledge Nowadays is getting more complex
    1. as more knowledge develops
      1. and since most knowledge is build upon each othe, it more complex as more required to know, making it more complex
    2. It is important to ask ourselves whether we approach a situation from a simplistic approach or complex one, most of the time one encompassing a complex one enompasses a more accurate one as it takes the whole picture into consdieration
  2. As knowers we try to seek the most simple appracoh/solution, as this is most likley to be better used when applied.
    1. This is characterized by the Occam's razor which is a problem-solving principle which was created by William of Ockham, his principle can be understand to mean that when deciding between which approaches to use, the one with the least assumptions should be used. I personally think he simply means that the simpler methodology should be used
      1. In my opinion fits perfectly with the scientific steps as less assumptions, generally imply more accuracy, however if more assumptions are neccasry then the accuracy is deminished
2. KQ: To what extent is there a trade of between simplicity and accuracy for the generation of KC using language and reasoning in the natural sciences and mathematics?
  1. Definitions of terms
    1. simplicity
      1. Being easily understood by someone with the core/basic knowledge, therefore has the least amount of assumptions
    2. accurate
      1. the state of representing reality, therefore containing the closest model of reality
    3. Mathematics
    4. Natural Sciences
    5. trade of
      1. the overall position considering advantages
  2. Claim 1: Impact of degree of simplicity of language in Mathematics and Natural Science on their accuracy
    1. Claim 1: For mathematics the degree of simplicity doesn't impact its accuracy, both simple and complex language results in accurate results. For example proving the pythagerous theorem using squares is very simple and accuarte, however if we prove it using by using vectors dot products it is more complciated (also includes an assumption) however equally valid. This is because the methodology of mathematics allows us to take different approaches and reach the same conclusion, in this case that a^2+b^2+c^2. This as mathematics isn't subejctive. In the Natural Science this is not the case, this as using simplistic language does impair the accuracy of the findings. For example in my Physics IA, I investigated the nature of a half life of a bouncing ball, if I were to explain my finidngs accurately I would have to use more complicated language. For example it would have to explain that the kinetic energy dissipates as the ball comes in contact with the ground, as work is done against
    2. Counter claim 1: General in mathematics the more complicated proofs show their claim to a stronger extent, due to nature allow a greater amount being proven. For the same example of proving the pythagoras, using vectors it proves the theorem for n dimensions, while the one using geomtric properties of squares only does this for the second dimension. For the natural sciences it is possible for simple language to accurate, however in this instance the use complex of lanugage is equally valud. These instance are when the complex model are simple adding extra information which does not impact the knowledge gain from an experiment/paper, for example If I were to measure the measure the surface area of particles reacting, the result wouldn't change no matter the representation using language, as it is still the approach which determines it .
    3. the kinetic energy, causing the energy to be reduced (could be shown mathematical), this is lost at a rate sp that the maximum height can be modelled as an exponential function, it is far more accurate represented and understand then simply saying the ball gets slower because it hits the ground.
  3. Impact of degree of simplicity of reasoning in Mathematics and Natural Science on their accuracy
    1. Claim 2: In natural science simple reasoning can lead to inaccurate results. This as some significant assumptions may be excluded during the simplification process, so only a cropped picture is viewed. For example If I were to take the simple approach of not changing the temperature for measuring the impact of concentration on an equilibrium reaction, it would be inaccurate because if I used different pressures, if the reaction were which gases particles, it would impact our result as it impacts the equilibrium position. This would cause a significant impact on our accuracy as other variables are impacting thhre results if they are not considered in the assumptions and therefore controlled. In mathematics the complexity of the assumptions does not matter, as the nature of mathematics, using axioms and postuales allows it to work in multiple different ways. For example when we assume
    2. Counter claim 2:
      1. However in some cases this does not matter in the natural sciences are the complex assumption may be insignificant in the accuracy, as they hardly impact for the accuracy to take a big hit. For example when measuring the magnetic field strength of a large telsa value, considering the uncertainty caused by the earth own magnetic field is insigiciant and would not change the results enough for it to matter.
      2. While generally in mathematics, simplicity o assumptions does not matter, however in the mathematical field of mathematical modelling, it does. For example in my Math IA, I attempted to model Volcanic eruption using the Poisson Distribution, for which certain assumptions must be taken into consideration, due to the length it was constraints of page length and time, it was slightly reduced to be simpler when considering assumptions. If I were to only take the simpler version of the assumptions, I would not check that the volcanoes are independent of each other but only independent from time between eruptions, if they were depends the whole knowledge gained from an investigation would be rendered useless, as the Poission distribution could not be used. Another example would for investigating the success of people through a mathematical model, we would be faced with a high degree of inaccuracy, as in this case there are too many variables which can be considered and assumptions
3. AOKs
  1. Natural Sciences
    1. NS aims is to understand our observable universe by exploring its laws and through experimentation.
  2. Mathematics
    1. study of quantities, shapes
    2. It is based upon axioms and postulates, which are taken to be universally True and self evidence. From this through the use of deductive reasoning, new mathematical truths can be found. This makes it more reliable in nature.
4. WOKs
  1. language
    1. Language is the method of communication, either spoken or written or through body gestures.
  2. Reasoning
    1. Can be defined as the use of deductive statements from assumptions to arrive at valid and logical conclusion based on the assumptions, these statements are very dependent on the assumptions as they are deduced from them
5. Other
Conclusion
1. When dealing with mathematical models the nature of the relationship of mathematics and simplicity along with accuracy mirrors that of natural sciences, as the more complex the better
2. In the natural science generally the more complex the better, however in some cases it does not matter.
  1. Therefore it is important for one to consider all the assumptions and make sure controlled variables s are kept controlled. The Nature of the scientific method supports this idea, by keeping on improving the experiment by making it more complicated
3. In mathematics the simpler proofs, are equally as valid, however they do not give as strong as a statement
4. From this it is important to consider the impacts of the uses of the different levels of complexities used, when creating an argument.
  1. because we re;ly on mathematics and the natural sciences in our daily life and it is important for them to be trustworthy
Key Terms
1. accuracy
  1. the state of representing reality, therefore containing the closest model of reality
2. simplicity
  1. Being easily understood by someone with the core/basic knowledge, therefore has the least amount of assumptions
    1. not based on length
  2. are they connected?
3. trade-off
  1. balance between positives and negatives
Things to inevtigate
1. Is accuracy different for everyone/all concepts
2. is simple knowledge the same for all aoks
3. are accuracy and simplicity related

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	Created by Lucas Alava Peña over 8 years ago