prior probability

I am totally serious. In honor of the upcoming Labor Day Holiday Weekend, allow me to pose the following (non-rhetorical) question: Why do we still allow the federal government (and many State governments) to tax our physical and mental labor, which is what an “income tax” basically amounts to? Go ahead and tax my capital gains, or my leisure activities, or my property, or my inheritance, or my wholesale or retail purchases, but for goodness’ sake, stop taxing my labor! Simply put, I don’t need a bunch of fancy jargon to obfuscate the self-evident truth that taxing people’s work is regressive and unjust–the moral equivalent of theft or forced labor. At the very least, the first $100,000 of one’s earnings should be tax free. What am I missing here? (PS: If you Google the phrase “abolish the income tax,” some very interesting things will pop up!)

“I am so sorry, but …” Although the “random excuse generator” pictured below (play around with it here for yourself; hat tip: @pickover) is quite crude–awkward even–it does a fairly decent job of coming up with good excuses! Maybe if this random excuse generator combined forces with an online writing assistant like “Grammarly” it could revolutionize the business and academic communities, where so much time is wasted in unproductive meetings.

Via Kottke: “MIT’s biology department is offering a new online class this fall called COVID-19, SARS-CoV-2 and the Pandemic. The class will be led by Richard Young and Facundo Batista and will include guest lectures by several leading authorities on Covid-19, coronaviruses, epidemiology, and immune systems like Anthony Fauci, Michael Mina, and Akiko Iwasaki. Here’s the course description and syllabus.”

A colleague recently brought to my attention this impressive list of 39 medieval universities founded before the year 1500 (hat tip: Dr Paul Jarley), though some of these venerable institutions have been closed for brief periods; for example, the University of Siena was closed 1805-1815 during the Napoleonic wars. Among other things, what I want to know is this: Did professors have academic “tenure” back then?

Check out these artworks by IndieTheIntrovert, including the one pictured below, which is titled “Escher’s Other Dogs.” FYI: M. C. Escher, one of the major inspirations of Douglas Hofstadter’s 1979 book Gödel, Escher, Bach, was a Dutch graphic artist who made mathematically-inspired art. Among other things, his work features mathematical objects and operations including “impossible objects” and explorations of infinity, and his work has appeared on the covers of many books and record albums. According to Wikipedia (see footnote 71 of this Wikipedia entry), Escher’s art became well-known among scientists and mathematicians, and in popular culture, after it was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American.

Here it is! (Pictured below are the first two pages of my new syllabus.)

Thinkers as diverse as Ludwig Wittgenstein, Thomas Kuhn, and Umberto Eco have used the concept of “family resemblance” to describe similarities among different objects/activities, so why not apply this concept to flags as well, such as those of Cuba 🇨🇺 and Puerto Rico 🇵🇷? The map below contains nine additional groups of national flags sharing close family resemblances.

Class #2 will be devoted to “The Blue Bus Problem” from the law of evidence. Harvard law professor Larry Tribe formulated this famous proof paradox over five decades ago as follows: “Plaintiff is negligently run down by a blue bus. The question is whether the bus belonged to the defendant. Plaintiff is prepared to prove that defendant operates four-fifths [or 80%] of all the blue buses in town. What effect, if any, should such proof be given?” Let’s call Larry Tribe’s hypo “Scenario A.” (This scenario is based on an actual case, Smith v. Rapid Transit, and is so famous in legal circles that it has generated numerous law review articles and taken up countless minutes in law school classrooms. I have previously surveyed this literature here.)

What if, however, the plaintiff is able to produce a witness, and what if the witness is prepared to testify that it was, in fact, the defendant’s blue bus that caused the accident? But what if the plaintiff’s testimony is reliable only 80% of the time? Let’s call this second hypo “Scenario B.” Either way, since the plaintiff in both scenarios is suing the defendant bus company for money damages (as is the case in most business disputes), the plaintiff is required to prove her case under “the preponderance of the evidence” standard. In plain English, in order to meet this standard, the plaintiff alleging a particular fact must prove that it is “more likely than not” that the fact is true.

Given this standard of proof, should the court rule for the plaintiff, or should it dismiss the case? Scenario A consists purely of statistical evidence or “naked probabilistic evidence” (e.g. the fraction of blue buses owned by the defendant), while Scenario B involves qualitative or “individualized evidence” in the form of eyewitness testimony, but the probabilities of accuracy are the same in both scenarios!