What is a Gaussian curve? In which situations can it accurately describe the world? Where does it fail, and what are its limits? The Gaussian curve is another name for the classic bell curve, or normal distribution curve. It’s named after German mathematician Carl Friedrich Gauss, and it describes many phenomena accurately. We’ll look at where the Gaussian curve is accurate and where (and why) it fails.
What is a dynamic system? What is dynamical systems theory? Why do dynamic systems make it so hard to make accurate predictions? A dynamical system (dynamic system) is one in which an array of inputs affect each other. Whereas prediction in a system that contains, say, two inputs, is a simple affair—one need only account for the qualities and behavior of those two inputs—prediction in a system that contains, say, five hundred billion inputs is effectively impossible. We’ll cover the most famous dynamic system examples and explore why dynamical systems make it so hard to make accurate predictions.
Who was Adolphe Quetelet? Why is he famous, and what was one of his biggest scientific mistakes? Adolphe Quetelet (Quételet) was a Belgian mathematician who developed the idea of the “average human” (l’homme moyen) through the use of “means”—golden averages that represented the ideal human form. He lived from 1796 to 1874. We’ll cover Adolphe Quetelet’s mistake in assuming that all phenomena can be charted on a bell curve and we’ll look at how we understand the world differently today.
What is Mediocristan? Where is it? Where does the word come from? What elements of our lives fall under the purview of Mediocristan? Mediocristan is a term coined by Nassim Nicholas Taleb to explain the facets of our experience that are nonscalable. Mediocristan’s law is: Given a large-enough sample size, no individual event will have a significant effect on the total. The term was popularized by Taleb’s book The Black Swan. We’ll cover what Mediocristan is, how it differs from Extremistan, and what kinds of events, characteristics, and professions come from the land of Mediocristan.
Does the bell curve accurately describe the world? When does the bell curve work, and when does it fail? How can we make better predictions and more accurately describe the phenomena of real life? We’ll cover the situations in which the normal bell curve distribution is a good predictor of the real world, the situations where it’s not, and better ways to represent randomness in an uncertain world.
What is scalability? How does scalability affect our lives? When is scalability a good thing? When is it a negative thing? Scalability is the characteristic or ability of a company or process to grow and adapt to changing demands. In the scalable parts of our lives, physical limits don’t apply and effects tend toward incredible extremes. We’ll further explore the scalability definition above, cover how scalability affects our lives, and cover which areas of our lives are most impacted by scalability.
What is a power-law distribution? How is it useful in describing and predicting events in the real world, which is full of uncertainty? Power-law distribution is a functional relationship between two quantities in which the relationship remains constant no matter the initial size of the quantities. This relationship is useful in describing events and phenomena that can’t be graphed on a bell curve. We’ll cover the basics of power-law distribution and look at how it works to accurately describe the world and account for otherwise unpredictable events.
What is a fractal? How are fractals useful in representing and predicting relatively unpredictable events? A fractal is a geometric pattern that repeats at different scales. Fractals, unlike pure geometric shapes like triangles or circles, are seen quite frequently in nature. We’ll cover what a fractal is and how it can help us make predictions in a world full of uncertainty.
What’s a grey swan? How does it serve as a metaphor for events that aren’t predictable, exactly, but imaginable? A grey swan (alternately, gray swan) is a term for events that can’t be predicted but can be imagined. It can also refer to an event that’s unlikely but possible. The term was popularized by Nassim Nicholas Taleb in the book Black Swan. We’ll cover what a grey swan is, how it fits in with black and white swans, and how to turn black swans grey.
What is the butterfly effect theory? How is it related to the idea of nonlinearities? How does it explain why we make bad predictions? The butterfly effect theory is the idea that a small change in a nonlinear system can have huge effects in the larger system. This idea was proposed by an MIT meteorologist, who discovered that an infinitesimal change in input parameters can drastically change weather models. We’ll cover what the butterfly effect theory is and how small changes can have large effects.