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.

The Pretense of Knowledge

Friedrich Hayek won the 1974 Nobel Prize in economics. This is from his acceptance speech:

To act on the belief that we possess the knowledge and the power which enable us to shape the processes of society entirely to our liking, knowledge which in fact we do not possess, is likely to make us do much harm. In the physical sciences there may be little objection to trying to do the impossible; one might even feel that one ought not to discourage the over-confident because their experiments may after all produce some new insights. But in the social field the erroneous belief that the exercise of some power would have beneficial consequences is likely to lead to a new power to coerce other men being conferred on some authority.

Later in the same speech:

The recognition of the insuperable limits to his knowledge ought indeed to teach the student of society a lesson of humility which should guard him against becoming an accomplice in men's fatal striving to control society - a striving which makes him not only a tyrant over his fellows, but which may well make him the destroyer of a civilization which no brain has designed but which has grown from the free efforts of millions of individuals.

HT: The Wall Street Journal.

Sam Rocha’s Strange and Startling Philosophy of Education

Stephen H. Webb's review of Sam Rocha's Primer for Philosophy and Education, in which Rocha

goes to some length to distinguish painting from priming, and as you read him, you realize that he is describing not priming but educating. He is showing his readers how education works by describing an analogous activity.