To what extent do you agree with the claim "all models are wrong, but some are useful" (attributed too George Box)? Discuss with reference to Mathematics and one other area of knowledge
Keywords
Model: An idealized / simplified, representation of a section of the world around us. It can simplify a physical, biological or sociological phenomenon
Useful: Can be use in the real life context to give insight, predict or solving the problem.
Why the PT is asked?
Real life example
Understanding the limitations of knowledge
Wrong: Refers to the inherent limitations and inaccuracies of models.
What the PT is asking?
Ideas on how to respond PT:
Mathematics:
Natural Sciences:
Exploring the nature of models across different areas of knowledge
All models will never behave the same as the reality as each model is bound to be somewhat off, obscuring certain facts of reality or highlighting others, missing some attributes while completely nailing others.
Critical reflection on the reliability of knowledge
Model can represent many things, including but not limited to objects that are too small to be observed with the naked eye, too big to see, objects that no longer exist. have yet to be invented or cannot be seen
Give perspective from both area of knowledge (strengths and limitations of the models)
Comparing mathematics and natural sciences
State your stand or to what extent do you agree
Provide real-life examples
Why do human still use the model eventhough it is wrong?
The purpose of models is usually to help visualise something that is difficult to explain with words or mathematical expressions. These models allow scientists help communicate their ideas and understand the process of a certain phenomenon.
What are models in Natural Sciences?
Scientific models are representations of objects, systems or events and are used as tools for understanding the natural world. Models use familiar objects to represent unfamiliar things.
How wrong should a model be to consider it not useful?
Is there such thing as a perfect model?
Examples
The Atomic models (Bohr's, Rutherford)
The Ideal Gas model, pV = NRT
The solar system
Mathematical models are quantitative and are usually expressed in ODE and PDE
Mathematical statistics are usually the most "useful" models.
A description of a system or phenomenon using the mathematical language
Examples
Epidemological modelling ( SIR Modelling, Bayesian Statistics )
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Normal distribution, Poisson distribution, Binomal distribution