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Intro Stats: Islamic Approach -- Part 2: Probability and Statistics -
Lecture 1: Random Samples, Concept 1: Models and Reality Slide 5: The Damgers of Using Models
5: The Dangers of Using Models
Even though we cannot avoid using models, we must recognize that there are MANY dangers when use simple models to represent a complex reality.
Models HIGHLIGHT some aspects of reality, and we focus on those aspects, but maybe these ARE NOT the most important. Automatically, they NEGLECT many other aspects, and maybe the neglected aspects are very important, but they are not part of our model so they become invisible to us. Because we tend to replace the complex reality by the simple model in our mind.
Quote from Nicholas Nessim Taleb: The Black Swan:
What I call Platonicity, after the ideas (and personality) of the philosopher Plato, is our tendency to mistake the map for the territory, to focus on pure and well-defined “forms,” whether objects, like triangles, or social notions, like Utopias (societies built according to some blueprint of what “makes sense”), even nationalities. When these ideas and crisp constructs inhabit our minds, we privilege them over other less elegant objects, those with messier and less tractable structures (an idea that I will elaborate progressively throughout this book).
Platonicity is what makes us think that we understand more than we actually do. But this does not happen everywhere. I am not saying that Platonic forms don’t exist. Models and constructions, these intellectual maps of reality, are not always wrong; they are wrong only in some specific applications. The difficulty is that a) you do not know beforehand (only after the fact) where the map will be wrong, and b) the mistakes can lead to severe consequences. These models are like potentially helpful medicines that carry random but very severe side effects.
The Platonic fold is the explosive boundary where the Platonic mindset enters in contact with messy reality, where the gap between what you know and what you think you know becomes dangerously wide. It is here that the Black Swan is produced.
Many examples of problems arising from the use of simplified models are discussed and illustrated by vivid real life examples in The Black Swan, by Nicholas Nessim Taleb. People calculate and make business plans, but COMPLETELY UNEXPECTED, IMPROBABLE events happen to upset all such plans. Nonetheless, equipped with model, people feel a false sense of security that they have calculated all the risks.
Nicholas Nessim Taleb; The Black Swan
NNT writes that in Las Vegas
Before the discovery of Australia, people in the Old World were convinced that all swans were white, an unassailable belief as it seemed completely confirmed by empirical evidence. The sighting of the first black swan illustrates a severe limitation to our learning from observations or experience and the fragility of our knowledge. One single observation can invalidate a general statement derived from millennia of confirmatory sightings of millions of white swans. All you need is one single (and, I am told, quite ugly) black bird.
What we call here a Black Swan (and capitalize it) is an event with the following three attributes.
First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.
I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability.[2] A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives. Ever since we left the Pleistocene, some ten millennia ago, the effect of these Black Swans has been increasing.
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