Wednesday Wisdom

WHO?

Thomas Bayes was a mathematician, philosopher, and Presbyterian minister from Sheffield England. In 1719, he enrolled in the University of Edinburg to study Logic and Theology. He followed his father Joshua's calling to become a Presbyterian minister where he was stationed in Kent outside London. His interest in philosophy, logic, and faith brought him into contact with many intellectuals of the "Royal Society". In 1742 he was elected into the prestigious "Fellows of the Royal Society", which is an organization to promote math and science. It is believed that his interest in probability was in response to Scottish philosopher David Hume's book "In Enquiry Concerning Human Understanding". Through empiricism and skepticism, Hume tries to explain the role of human testimonials when exploring miracles. Bayes tries to take this notion one step forward by creating a mathematical formula. His essay “Essay Towards Solving a Problem in the Doctrine of Chances” was released posthumously several years after his death.

What he produced

In 1990 in Parade magazine segment titled "Ask Marilyn", Marilyn von Sant was asked a question by a reader that incited an academic firestorm.

The question posed as this: "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?" This is known as the Mony Hall problem.

Von Sanst response was you always switch because you increase your odds from 50pct to 66 pct. The response was fierce and even derogatory from some of the smartest academics and mathematicians. The outcry to von Savant’s response was so tremendous that she was forced to devote three subsequent columns to explaining why her logic was correct. Even in the wake of her well-stated, clear responses, she continued to be berated. “I still think you’re wrong,” wrote one man, nearly a year later. “There is such a thing as female logic.” According to the majority of responses, switching doesn't help since your odds are always 50/50,

Bayes produced a mathematical theorem to show the probability of outcomes when multiple variables were introduced. If "A" happens, what is the probability of an outcome? Probability calculations become more difficult when another or multiple variables are added. Bayes Theorem gives us a way to calculate the output through a formula of P(A)(B)= P(A)/P(B)*P(A)/P(B) where calculate the (P) probability of event (A) and event (B). Each new piece of information affects and changes the outcome probability. The right answer is to switch, since your odds increase from 1/3 or 33% to 2/3 or 66%. The data below maps out all the scenarios:

2022: Why do we care?

The logic behind Bayesian statistics is at the core of almost every modern estimation approach that includes conditioned probabilities. The use of data has become more prominent across all industries as they assess future risks and outcomes. This includes data-driven computer programs like sequential estimation, probabilistic machine learning techniques, risk assessment, simultaneous localization and mapping, regularization, or information theory which are all based on Bayes Theorem.

Using this formula isn't exclusive to big data and large computation. There is a reasonable chance that you unknowingly rely on the Bayes Theorem every day in your decision-making. It can be as simple as searching for your car keys. Using previous experience, you would begin by eliminating the most likely location and then move on to the less probable one until you find your keys. When more information is presented, probabilities change and so does our decision making.

As far as we know, Bayer never published his findings while he was still alive, so he probably never realized the scope of his work. However, as we move to a more data-driven world, Thomas Bayes' legacy lives on.

And now you know....

Philosophy is the art of thinking, the building block of progress that shapes critical thinking across economics, ethics, religion, and science.

METAPHYSICS: Literally, the term metaphysics means ‘beyond the physical.’ Typically, this is the branch that most people think of when they picture philosophy. In metaphysics, the goal is to answer what and how questions in life. Who are we, and what are time and space?

LOGIC: The study of reasoning. Much like metaphysics, understanding logic helps to understand and appreciate how we perceive the rest of our world. More than that, it provides a foundation for which to build and interpret arguments and analyses.

ETHICS: The study of morality, right and wrong, good and evil. Ethics tackles difficult conversations by adding weight to actions and decisions. Politics takes ethics to a larger scale, applying it to a group (or groups) of people. Political philosophers study political governments, laws, justice, authority, rights, liberty, ethics, and much more.

AESTHETICS: What is beautiful? Philosophers try to understand, qualify, and quantify what makes art what it is. Aesthetics also takes a deeper look at the artwork itself, trying to understand the meaning behind it, both art as a whole and art on an individual level. A question an aesthetics philosopher would seek to address is whether or not beauty truly is in the eye of the beholder.

EPISTEMOLOGY: This is the study and understanding of knowledge. The main question is how do we know? We can question the limitations of logic, how comprehension works, and the ability (or perception) to be certain.