Pope Francis on the Feast of St. Stephen

From Pope Francis’ Angelus address for the Feast of Saint Stephen, 26 December 2014:

To truly welcome Jesus in our existence, and to prolong the joy of the Holy Night, the path is precisely the one indicated in this Gospel: that is, to bear witness in humility, in silent service, without fear of going against the current, able to pay in person. And if not all are called, as Saint Stephen was, to shed their own blood, nonetheless, every Christian is called in every circumstance to live a life that is coherent with the faith he or she professes.

Where to stay in Blacksburg, Virginia

We can recommend two very different bed-and-breakfasts in Blacksburg, Virginia: The Huffman House at Creekside Farm in the mountains west of town and the Clay Corner Inn just a few blocks from downtown and the Virginia Tech campus. At both places we found friendly hosts, very comfortable rooms, and delicious breakfasts.

How to Find a Spouse

From First Things, an article by Betsy VanDenBerghe on what is truly important when looking for a spouse. She lists the five factors that John Van Epp (author of How to Avoid Falling in Love with a Jerk), says are essential to consider in a relationship:

• compatibility in familial, religious, and financial values and priorities,
• communication skills like self-disclosure, mutual assertiveness, and ability to apologize,
• behavior in other relationships,
• patterns of family background, and
• a healthy conscience (neither underactive nor overactive).

The Way of Aporia

In her article Uneasy Grace, Meghan Sullivan discusses four approaches to resolving struggles between Christian faith and other evidence:

1. On the Way of Dilution, one gives up things one believes.
2. On the Way of Fundamentalism, one refuses to reason and dismisses the other evidence without thought.
3. On the Way of Separation, one keeps the two types of beliefs completely separate and does not try to reconcile them.
4. On the Way of Aporia, one accepts that one's understanding is limited and works to resolve the conflict while accepting both types of beliefs until understanding arrives.

According to Sullivan,

there are some conflicts that we never get to resolve in this life. At the heart of the Way of Aporia is a conviction that you shouldn’t ignore conflicts between faith and reason. They are bound to happen, especially if you have a valuable, thick faith. But you also should not give up important beliefs too quickly or too flippantly in the face of conflict. This is a perfectly respectable stance in other branches of inquiry. And it is perfectly respectable for Christians to assume.

Georgia Tech's Official Colors

Although "Up with the White and Gold" is the best fight song ever, Tech's official colors are not white and gold. According to the Official Colors page:

Authorized colors are gold (PMS 124), navy (PMS 539), metallic gold (PMS 874), and black.

Modeling the ski rental problem

In the ski rental problem, the decision-maker (let’s call him Joe) is going to spend multiple days skiing. He can purchase a pair of skis for a price of $K and use them one or more days (including the day on which he purchases the skis). He can also rent a pair of skis for one day for $1. (He won't rent skis if he has purchased some.) He can rent skis as many times as he wants. The critical assumption is that Joe has no idea how many days he will go skiing; he will ski until something stops him – an injury, bad weather, a loss of interest, or something urgent at home or work, for example – but he does not put a probability distribution on the number of days that he will ski.

What is interesting is that there are two ways to model the problem. The first model assumes that, before day 1, Joe will select a day (D) on which he will purchase skis if he is still skiing that day, but he will rent skis every day until then. Thus, if he skis a total of N days, then his total cost for skis equals N if N < D, and D – 1 + K if N >= D. This version seems to capture the risky nature of the decision. Selecting a small value of D is bad if N is only slightly larger than D; selecting a large value of D is bad if N is close to but not greater than D. (Small and large are relative to K.)

The second model considers the sequential nature of the problem: if Joe rented skis on the one day, then he has a decision to make the next day (rent again or purchase). Interestingly, there seems to be a memoryless property here: because Joe has no idea how many days he will ski, then he has no idea how many more days he will ski, so the decision on every day is the same. If he decides to rent a pair of skis on Day 1, he should rent a pair of skis every day, for there is no reason to change his choice. If, on any day, he would decide to purchase a pair of skis, then he should do that on Day 1. This would imply that Joe’s only reasonable choices are to purchase a pair of skis on Day 1 or never.

I suspect that I’ve run into a situation that occurs in other infinite-horizon sequential decisions. If so, I’d love to know which model is more reasonable and why.

Catholic Education, the Common Core and the New Evangelization

An interview with the executive director of the Secretariat of Catholic Education about the Common Core.