Apr 15, 2018 - Paradoxes, Probability    No Comments

Boy or Girl Explained

The “Boy or Girl Paradox” (also called “The Two Child Problem” in addition to other names) is generally phrased as follows:

You know a couple who has two children. At least one of the children is a girl. What is the probability that they have two girls?

This is an ambiguous problem, which leads to different answers depending on the assumptions that are used. Not enough information has been provided to produce a definite answer, and the unstated assumptions fill in the space needed to complete the logic.

Here I investigate this problem and explain the ambiguity.

[Boy or Girl?]
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Nov 18, 2016 - Education, Politics    1 Comment

Fearing for the Future

While this report doesn’t explain the results of the recent election, it might explain the reaction to the election that we’re seeing at colleges and universities nationwide. This goes beyond just “safe spaces” and “trigger warnings.” Offering majors in basket weaving and “[fill-in-the-blank] studies” is doing nothing for the competitiveness of the US in the world market of ideas.

Think about this the next time someone (particularly a millennial) tries to tell you that “educated people” think this or think that. This report indicates that they don’t have the proper analytical skills to have an informed opinion (compared to most of their international peers or to previous generations), even the ones with the highest degrees.

Pay particular attention to the part that addresses “years of schooling” and “conferring of credentials and certificates.” Anyone who thinks that Sanders’s plan for “free college” would to do anything to help the country or the economy is fooling himself.
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Sep 1, 2015 - Numbers    Comments Off on Number Magic – An Explanation of Bendford’s Law

Number Magic – An Explanation of Bendford’s Law

Earlier this year, a colleague of mine sent me an email on Bendford’s Law. He had run across it somewhere and was fascinated by it. It seems counterintuitive that small digits would occur more frequently in the leading digits of arbitrary numerical data. One is tempted to think that arbitrary data would be made up of arbitrary digits, but that turns out not to be the case. It’s a genuine numerical phenomenon, and below I have provided a couple of ways to explain it. I point out that, utlimately, this law results from the notation that we use to represent real values.

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Aug 30, 2015 - Paradoxes, Probability, Statistics    Comments Off on Sleeping Beauty Plays the Lottery

Sleeping Beauty Plays the Lottery

I’ve already examined the classic Sleeping Beauty Problem and pointed out some of the pitfalls that many people fail to avoid when trying to solve the problem. I also examined Nick Bostrom’s so-called “Extreme Beauty” modification to the problem, in which Beauty wakes many, many times if the coin toss comes up tails. However, there is another “extreme” variant of this problem, the variant in which the coin toss is replaced with another two-result random process that has extremely uneven odds. That is, in this “extreme” problem, one of the possible results is extremely unlikely. Examining this variant with the methods of reasoning commonly used by the “thirders” can be enlightening and can provide some illustration of why they are wrong.

Since many “thirders” seem to be fond of relying on betting analogies to reason through the problem and explain their arguments, a useful substitute for the coin toss is a lottery. A typical lottery provides a very small chance of winning accompanied by a very large payoff (which is why lotteries are so popular). So here we shall examine what happens when Sleeping Beauty plays the lottery.

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Sleeping Beauty

For over 15 years, some people—particularly philosophers—continue to be confused by the so-called “Sleeping Beauty Problem.” This is a rather straight-forward exercise in conditional probability that should be accessible to a student in an undergraduate course on probability and statistics. Nevertheless, there are people who have managed to arrive at the wrong answer to this problem.

[Image from http://www.wikihow.com/Draw-Sleeping-Beauty]
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May 27, 2015 - Sports & Leisure    1 Comment

Dan’s Idaho Nuclear Chili

This is a recipe that comes compliments of Dan Yurman, which I have copied from his blog. Since his original blog completed its run and has since vanished from the Internet, I thought it would be wise to preserve a copy his recipe here, in case his latest blog also eventually goes away. Enjoy.

In the spirit of Thanksgiving, and wanting to take a break from reading, thinking, and writing about nuclear energy, I’m offering my tried and true cooking instructions for something completely different.

By Sunday night you will be stuffed, fed up, literally, and figuratively, with turkey. Instead of food fit for pilgrims, try food invented in the wide open west—chili. Cook this dish on Saturday. Eat it on Sunday.

These instructions take about an hour to complete. This chili has more vegetables and beans than some people might like, but we’re all trying to eat healthy. Although the name of this dish has the word “nuclear” in it, it isn’t that hot on the Scoville scale. If you want some other choices for nuclear chili there are lots of recipes on Google

The beer adds sweetness to the vegetables, as does the brandy, and is a good for cooking generally. In terms of the beer, which is an essential ingredient, you’ll still have five cans or bottles left to share with friends so there’s always that.

However, I recommend Negra Modelo for drinking with this dish and Budweiser or any American pilsner for cooking it. Alternatives for drinking include local western favorites, Moose Drool or Black Butte Porter, and regional amber ales Alaskan Amber, Fat Tire, or Anchor Steam. Do not cook with “light” beer. It’s a very bad idea.

History of the cooking instructions

Scoville, Idaho, is the destination for Union Pacific rail freight for the Idaho National Laboratory (INL) way out on the Arco desert.

There is no town by that name, but legend has it that way back in the 50s & 60s, when the place was called the National Reactor Testing Station, back shift workers on cold winter nights relished the lure of hot chili hence the use of the use of the name “Scoville” for shipping information.

Overnight temperatures on the Arco desert can plunge to −20 °F or more. Unfortunately, the guys running the reactors couldn’t drink beer, but they did have coffee. It’s still that way today.

Why “Second-day” in the name?

This is “second-day chili.” That means after you make it, put it in the unheated garage to cool, then refrigerate it, and reheat the next day. The flavors will have had time to mix with the ingredients, and on a cold Idaho night what you need that warms the body and the soul is a bowl of hot chili with fresh, warm cornbread on the side.

If you make a double portion, you can serve it for dinner over a hot Idaho baked potato with salad. Enjoy.

Dan’s Second-Day Idaho Nuclear Chili


1 lb chopped or ground beef (15% fat)
1 large onion
1 sweet red pepper
1 sweet green pepper
10–12 medium size mushrooms
1 can pinto beans (plain, no “sauce”)
1 can black beans
1 can chopped tomatoes
1 can small, white “shoepeg” corn
1 12 oz can beer
1 cup hot beef broth
1 tablespoon cooking brandy
2 tablespoons finely chopped jalapeno peppers
2–4 tablespoons red chili powder
1/2 teaspoon black pepper
1/2 teaspoon salt
1/2 teaspoon coarse powdered garlic
1/2 teaspoon cumin


  1. Chop the vegetables into small pieces and brown them in cooking
    oil. Add 1 tablespoon of cooking brandy near the end. Drain thoroughly.
  2. Brown the meat separately and drain the fat.
  3. Combine all the ingredients in a large pot. Be sure to drain the
    beans, and tomatoes before adding. Simmer slowly for at least
    60–120 min. Stir occasionally.
  4. Set aside and refrigerate when cool.
  5. Reheat the next day. Serve with cornbread. Garnish with shredded
    sharp cheddar cheese.

Feeds 2–4 adults.

Aug 23, 2014 - Sports & Leisure    Comments Off on The Virginia Cocktail

The Virginia Cocktail

This is a cocktail that I created while I was in graduate school. I named it “The Virginia Cocktail” (or a “Virginian” for short), because I created it while living at the University of Virginia. Basically, it’s an old-fashioned martini (some early recipes for the martini specified orange bitters) with a tomolive as the garnish. A tomolive is a small, pickled green tomato, not much larger than a large olive.

Although I recommend stirring the drink and serving it straight up, when I first used to enjoy this drink, while living at 4 East Range in the “Academical Village,” I used to drink it on the rocks for practical reasons. Those venerable rooms at UVa don’t even provide a toilet, much less a kitchen or wet bar, so I had only a compact, dorm-sized fridge to provide the limited amount of ice that I had available for making drinks.

The recipe is as follows:

  • 8 parts gin
  • 1 part French vermouth
  • a dash of orange bitters
  • one tomolive

Mixed (preferred):

In a mixing glass half filed with cracked ice, add a dash of orange bitters. Then add the vermouth and gin. Stir until cold. Strain into a chilled cocktail glass. Add the tomolive and serve.


Fill a chilled cocktail glass with ice and vermouth. In a shaker filed with cracked ice, add the dash of orange bitters and the gin. Shake until cold. Dump the ice and vermouth from the glass, and strain the shaker into the glass. Add the tomolive and serve.

Mar 3, 2014 - Climate, Statistics    Comments Off on Warming or Walking? – Stochastic Processes and Temperature Trends

Warming or Walking? – Stochastic Processes and Temperature Trends

Of all of the statistics that are cited to support the notion of “global warming,” the one that bothers me the most is the statistic claiming that \(n\) of the last \(m\) years have been the hottest years on record. For example, it’s not uncommon to hear that “10 of the last 12 years” are the warmest years in a temperature record that goes all the way back to 1880. This is often used as “irrefutable evidence” that mankind is driving up the Earth’s temperature and destroying the planet.

It is understandable that an activist would try to exploit this statistic. Most obviously, it emphasizes that recent global temperatures have been relatively high (where “high” corresponds to an increase of less than one degree Celsius over a 100-year period). The real purpose of repeating this factoid, however, is that it confuses and charms the numerically unsophisticated, leading them to assume that such a concentration of unprecedented, elevated temperatures in recent times is highly unlikely—unless some underlying cause is responsible.

This is quite misleading, however. In fact, it is not difficult to demonstrate that a relatively simple statistical model can account for this result, without requiring any bias toward warming.

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