Please enable JavaScript.
Coggle requires JavaScript to display documents.
CHAPTER 15 - Coggle Diagram
CHAPTER 15
THE GAUSSIAN AND THE MANDELBROTIAN
The Increase in the Decrease
in Gaussian,the odds dramatically increase in decline as the numbers move away from the average
This allows to ignore outliers
The Mandelbrotian
Scalable=Mandelbrotian
The Gaussian curve doesn’t take extremes into account, but the Mandelbrotian curve does
Inequality
Inequality among super-rich is same as the inequality among simply-rich
In estremistan, divisions of some total are asymmetric
What to Remember
Gaussian bell curve's probabilities drop at increased rate as moving away from the average; while Mandelbrotian variations don't have such restriction
Extremistan and the 80/20 Rule
80% of outcomes (e.g. work) result from 20% of all input (e.g. people)
It was proposed by Vilfredo Pareto
Grass and Trees
Unpredictable large deviations can not be dismissed as outliers because their cumulative impact is dramatic
Two varieties of randomness
One is impacted by extremes and generate Black Swans
Other doesn't care about extremes and do not generate Black Swans
If there are strong forces of equilibrium bringing things back after divergence, than we can use Gaussian approach
How Coffee Drinking Can Be Safe
The safety of the coffee cup (it will not jump spontaneously and the coffe will not be spilled without our intervention) represents how randomness of the Gaussian is tamable by averaging
Love of Certainities
The standard deviation, correlation and regression only exist in the Gaussian family, outside of that they are meaningless
How to Cause Catastrophes
Term "statistically significant" used in statistics give an illusion of certainities
QUETELET'S AVERAGE MONSTER
On the title
The bell curve is the work of the French Calvinist Abraham de Moivre
Adolphe Quetelet came up with idea of a physically average human
Golden Mediocrity
Quetelet's physically and morally average man made everyone, that are to the left or right of the average "normal" man (average of Bel's curve) - abnormal
This is unlogical pursuit of thinking as the notion of a man deemed average is different from that of a man who is average in everything he does
God's Error
Gaussian distribution was used as distribution of errors in astronomic measurements
Divergence from the mean was treated as an error, this was inprinted on the thoughts of contemporary socialist
Poincare to the Rescue
Gaussian was initially meant to measure astronomic errors, and Poincare's ideas of modeling celestial mechanics were fraught with deeper unceratinity
Eliminating Unfair Influence
Reality is not Mediocristan and we should learn to live with it
"The Greeks Would Have Deified It"
Sir Francis Galton, Charles Darwin's first cousin, might have contributed to the prevalence of the Gaussian curve as he was so excited about it that he thought Greeks would have deified Gaussian curve
"Yes/No" Only Please
If we have some qualitative inference and we are looking for yes/no answers to which magnitudes don't apply, we can assume that we are in Mediocristan
A (LIBRARY) THOUGHT EXPERIMENT ON WHERE THE BELL CURVE COMES FROM
Those Comforting Assumptions
Central assumptions in the coin-flip game: 1) the flips are independent of one another and the coin has no memory; 2) there is no wild jump
If these two central assumptions are not met, coin tosses wil not lead to the bell curve
"The Ubiquity of the Gaussian"
Technique (to not make the same errors of platonifying) is to know the bell curve as much as one can and to identify where it can and where it cannot hold
On the title
The main point of the Gaussian bell curve is that the most observations hover around the mean, while the odds of deviations decline faster as you move away from the mean
CONCLUSIONS
Uncertainty in Mediocristan vanishes under averaging
Gaussian bell curve is the curve of Mediocristan, and Mandelbrotian curve better takes into account the extremes
The reason why we like the Gaussian curve is that it is predictable
WHAT TO EXPECT NEXT
Proofs that Gaussian bell curve is not ubiquitous
The properties of the fractal
More about Benoit Mandelbrot's thoughts and ideas about reality