Day 3: mat385

Last time

Next time

Today:

• Announcements:
  • I hope that you had an enjoyable and restful MLK, Jr. Day. My wife works in health care, and for her it was just another day; but I had the luxury of listening to a few of King's speeches. Wow.

    Listening to him read his Letter from a Birmingham Jail was very moving.

  • Keep up with the homework! Your first assignment is due today at midnight. Email with questions, or post to the discussion.

    Please save your work as a single pdf (lots easier for me to grade), and upload that to Canvas. (Thanks to Jacob for prompting me to add the assignment to Canvas, so you have a place to upload it!)

  • You have a new assignment, which will be due a week from today.

  • Some of you may have wondered about that Mensa question, about the probability of tossing a head (given that one has already tossed 17 heads in a row).

    Bayesian statisticians update probabilities as they learn more, and I would consider myself a Bayesian. So when I see a coin tossed heads 17 times in a row, my conclusion is that the coin is unfair (even if not two-headed -- but if it were two-headed, it would certainly be unfair!).

    The probability of tossing a fair coin and having it land heads (or, symmetrically, tails -- one or the other) 17 times in a row: $2\left(\frac{1}{2}\right)^{17} \approx .0000153$

    That's less than 1 in 50000 times. It ain't chance folks: it's a fix! (Well, it could be chance -- it's just so unlikely that we accept the much more plausible hypothesis of cheating.)

    Occam's razor says: the simplest consistent explanation is usually the right one. This is a type of logic, as well.

• Last time: we continued with Section 1.2: Propositional Logic: proving "theorems" in the form of wffs with implication as their main connective:
  • 1.2, Part I
  • 1.2, Part II
  • The marked up pdf

• More falsehoods, from which anything can be proven:

  NPR reports that Trump's Census Director To Quit After Trying To Rush Out 'Indefensible' Report:

  • This month, while the bureau was continuing work on the latest state population counts, Dillingham attempted to pressure career employees to make a technical data report about "documented and undocumented persons" a "number one priority" to be produced by Jan. 15, according to a memo by the inspector general's office at the Commerce Department, which oversees the bureau.

  • Dillingham's push for the data in the final days of the Trump administration came to light after whistleblowers at the bureau warned that the report would be "statistically indefensible" and could be "misinterpreted, misused, or otherwise tarnish the Bureau's reputation." (My emphasis)

  • The point is that, if we can get falsehoods entered into "the official record", we can use those to bootstrap our way to anything. Beware this type of attack! Otherwise you'll end up with Bertrand Russell as Pope...:)

• Today: we'll hit Highlights of Section 1.3: Quantifiers, Predicates, and Validity
  • 1.3, Part I
  • 1.3, Part II
  • The marked up pdf

• Links:
  • Nothing new at the moment.