COVID Testing and Bayes’ Theorem

Yesterday, an interesting conundrum came to me. Sometimes, people take two COVID tests on the same day. Imagine that one came back negative and the other came back positive… which can and does happen. Here is the tricky question… which one do you trust? The positive or the negative? You might think there is noContinue reading “COVID Testing and Bayes’ Theorem”

“The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner (Summary & Comments)

It is only relatively recently in human history that the deep connection between math and physics was realized. Early civilizations knew of some simple connections regarding a pretty intuitive level of mathematics. Counting has an obvious connection to our world, as does much of geometry. And yet, that isn’t really what science is any more.Continue reading ““The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner (Summary & Comments)”

Critical Thinking Toolkit: Weighing Evidence with Bayes’ Theorem

When we are involved in important discussions, it is important to not take pivotal claims of others – or ourselves – merely at face value. Instead, we debate the various available ideas. That is, we bring forth evidence that we have thought about and that we believe supports our position, and we listen to theContinue reading “Critical Thinking Toolkit: Weighing Evidence with Bayes’ Theorem”

Do “Monkey-Typewriter” Arguments Work?

There is a famous analogy that is used in discussion of highly improbable events – that of monkeys sitting at a typewriter, banging away at the keys. It is said in this parable that, given enough time, the monkey will type out Hamlet, or a Shakespeaean sonnet, or the complete works of Shakespeare, or someContinue reading “Do “Monkey-Typewriter” Arguments Work?”

How Would We Know COVID-19 is in Decline?

In light of the current COVID-19 pandemic, I have written an article entitled How Does Disease Spread? in which I discuss how mathematicians attempt to understand the way that a virus is spreading in the population. In said article, my primary focus is building up the concepts and thought processes that are needed to understandContinue reading “How Would We Know COVID-19 is in Decline?”

How Does Disease Spread?

These are difficult times. Because of the spread of the COVID-19 virus, we are all taking very drastic measures to ‘flatten the curve’ by socially distancing, increasing our awareness of hygiene, and many other measures. These, of course, should be done, because lives will be saved. But how, exactly, do we know this? We don’tContinue reading “How Does Disease Spread?”