and since most knowledge is build upon each othe, it
more complex as more required to know, making it more complex
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
As knowers we try to seek the most simple appracoh/solution,
as this is most likley to be better used when applied.
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
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
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?
Definitions of terms
simplicity
Being easily understood by someone with the core/basic
knowledge, therefore has the least amount of assumptions
accurate
the state of representing reality, therefore containing the closest model
of reality
Mathematics
Natural Sciences
trade of
the overall position considering advantages
Claim 1: Impact of degree of simplicity of language in Mathematics and Natural Science on their accuracy
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
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 .
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.
Impact of degree of simplicity of reasoning in Mathematics and Natural Science on their accuracy
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
Counter claim 2:
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.
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
AOKs
Natural Sciences
NS aims is to understand our observable universe by
exploring its laws and through experimentation.
Mathematics
study of quantities, shapes
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.
WOKs
language
Language is the method of communication, either spoken or written or through body gestures.
Reasoning
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
Other
Conclusion
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
In the natural science generally the more complex the better, however in some cases it does not matter.
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
In mathematics the simpler proofs, are equally as valid, however they do not give as strong as a statement
From this it is important to
consider the impacts of the uses
of the different levels of
complexities used, when creating
an argument.
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
accuracy
the state of representing reality, therefore
containing the closest model of reality
simplicity
Being easily understood by someone with the core/basic knowledge, therefore has the least amount of assumptions