P&S L1 C5 S3

Intro Stats: Islamic Approach -- Part 2 Prob & Stat

Lecture 1: Random Samples -- Concept 5: Law of Large Numbers

S3; Probability as a Metaphor-Model

We now provide a new definition of probability as a model -- very separate and distinct from reality.

A "metaphor" says that two thing which are COMPLETELY different are the same: LIFE is a Roller-Coaster. All metaphors are always literally false. Nonetheless, they often convey deep insights.

A MODEL sets up a correspondence between an idealized, abstract, mathematical entity, and the complex, qualitative and non-mathematical real world. This is why famous statistician Box said that "All models are wrong, but some are useful". Model are always literally false. But matching the model with reality allows us to make some computations which are helpful in understanding some aspects of reality. When these calculations work VERY WELL, there arises the DANGER of confusing the model with reality. THIS HAS HAPPENED very often, and led to massive confusions, especially in the field of probability.

Important Consequence of the Metaphor View of Probability: Probability DOES NOT EXIST in the real world. When we say that the probability of the flipped coin coming up heads is 1/2, we are not talking about any property of the coin. RATHER, we are saying that a model of the coin as being a random draw from a box with {H,T} is a good way to look at the world for CERTAIN PURPOSES -- Since a metaphor is always false, we do not assert them as truths, but as being useful to achieve CERTAIN SPECIALIZED insights about the real world. A metaphor EMPHASIZES and BRINGS OUT SHARPLY certain aspects of reality. In the process of doing so, it NEGLECTS and SUPPRESSES other aspects. Thus the use of metaphors is always fraught with dangers.