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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.
- Maths
- Accuracy
- 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

- 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
- Simplicity
- 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.

- 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.
- KC1 - Accuracy of the statement is not affected by
the simplicity of the language
- mathematical notation,
universally agreed upon
symbols, one interpretation
- Not dependent on language used in maths
- Only dependent on logic and reasoning

- Only dependent on logic and reasoning

- Not dependent on language used in maths
- Ex. Area of triangle
- Half ab sin c
- Same Answer
Ultimately

- Same Answer
Ultimately
- Half bh

- Half ab sin c

- mathematical notation,
universally agreed upon
symbols, one interpretation
- CC1: simple mathematical models are
not enough to be an accurate
representation of reality
- Simplification sacrifices accuracy
- 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.

- 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.

- Simplification sacrifices accuracy

- Accuracy
- Natural Science
- Accuracy
- 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.

- 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.
- Simplicity
- 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.

- 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.
- 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.
- Use of language

- Use of language
- 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.
- Actual theory
- Different types of simplicity; simplicity in language,
and simplicity in the actual theory

- Different types of simplicity; simplicity in language,
and simplicity in the actual theory

- Actual theory
- AOK

- Accuracy
- Introduction
- Define
- Accuracy
- The quality or state of being correct (Oxford Dictionary)
- Correct: Representation of Reality

- Correct: Representation of Reality

- The quality or state of being correct (Oxford Dictionary)
- Simplicity
- the quality of being easy to understand
(Oxford Dictionary)

- the quality of being easy to understand
(Oxford Dictionary)

- Accuracy
- Knowledge
- Introduction
- RLS
- KQ
- TWE does the simplicity impact on the accuracy of the
knowledge conveyed in the AOKs of
Maths and Natural Science
- AOK
- WOK
- langugage

- langugage

- TWE does the simplicity impact on the accuracy of the
knowledge conveyed in the AOKs of
Maths and Natural Science

- Introduction
- Final Verdict
- See conc

- See conc

- Define
- Conclusion
- Sum of the Claims
- Linking to
Original Question
- There is never ALWAYS a trade
off between accuracy and
simplicity

- There is never ALWAYS a trade
off between accuracy and
simplicity
- So What
- 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

- 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

- Sum of the Claims
- If there is always a trade-off, should
we prefer accuracy over simplicity?
- Find a balance?

- Find a balance?

- Maths

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