Friday, January 29, 2016

On Certainty

Once it was part of my job to work alongside experts in Quality Assurance. Actually, many of my colleagues weren't experts, just go-getters willing to give QA their best shot. The experts weren't always the best at this work, either, because being really good at QA is partly a matter of temperament. Watching the QA team operate, I came to think that when it comes to checking a piece of work, there are two kinds of people: those who are trying to make sure the work is correct, and those who are trying to prove that it isn't. You want the second type of person on your QA team. A checker should revel in finding errors, not aim to show that there aren't any. 

If there are two mentalities, one corresponding to the jaded TSA employee and the other corresponding to the lovingly patient KGB interrogator, then I'm interrogatory by nature. But I do catch myself thinking the wrong way sometimes, such as when I'm finished putting away the pieces of a board game. 'Wouldn't it be nice, now (says my brain) to put on the box top and take the game back to the shelf!' Yes, it would be nice, but there is still another piece on the floor. Trust me, there is. One of my personal folk theorems is, 'There's always one more.' Need a paper clip or a rubber band? You're in luck, because there's one more in that drawer. Look long enough and you will find it. Nobody in history, to my knowledge, has ever run out of paper clips.

Another doctrine of mine is The Fundamental Theorem of Travel Delays, which I deduced circa 2010. This theorem says that The number of travel delays is not equal to 1. Corollary: If Delta Airlines, MTA, or Amtrak announces a delay, then start researching other plans, because they are going to announce another delay. Any other outcome would violate the theorem. Here is another example of the theorem in action: if you are entering a New York subway station, and if the person ahead of you swipes their MetroCard and gets an error message with a beep, then for the love of God, get yourself out from behind them. Where there is one beep, there will be another.

Even though I have the temperament for it, QA probably wouldn't be a good profession for me. I would spend too much time checking a piece of work when there were other pieces of work to be checked. There is such a thing as being overly perfectionist. Ignatius Reilly, the main character in the novel A Confederacy of Dunces, had a job pasting due-date slips into library books. "On some days," he said to his mother, "I could only paste in three or four slips and at the same time feel satisfied with the quality of my work." 

A paradox that made a strong impression on me as a child was the paradox of Caesar's dying breath. Every breath you take, so the saying goes, probably includes at least one air molecule from Caesar's dying breath. Amazing, isn't it? Although the probability is minuscule that any randomly selected air molecule boasts such a pedigree, nevertheless, a breath of air contains so many molecules that the chances of entirely avoiding the imperial ones are low. It's like playing Russian roulette with a gun that is nearly empty but pulling the trigger eighty sextillion times. There's no future in it. Similarly, in the design of population studies, sometimes you don't need your sample to be a large percentage of the population if the sample is large in absolute terms. Intuitions like these inform my neurotic approach to copy editing: while any given word is nearly certain to be correct, in a long enough run of words there must be errors.

Addiction therapists describe gamblers who think that if a game offers a player a one-in-four chance of winning, then the player is certain to win by playing the game four times. I created a much harder puzzle once to test the solver's sense of such things: if the probability of winning a game is the same as the probability of losing the game a million times in a row, then is the probability of winning the game less than, equal to, or greater than one-in-a-million? I find this puzzle challenging! But the belief about the game of one-in-four is so wrong, I cannot believe that anybody believes it. Somehow those therapists are tricking people into giving the wrong answer. That said, if you can easily be tricked into giving an answer that on second thought you realize is wrong, then the real problem is not your intuitions about probability—it's your neglect of the habit of giving second thoughts to things. To build this habit, it is necessary to err frequently.

Socrates was unsure of everything save his own power to sniff out error. To detect error, it helps to believe in it.  'Out of the crooked timber of humanity no straight thing was ever made.' Certainty is a state of mind normally denied us, but if there is one thing we can be sure of it's mistakes. Between us, I despair of proofreading this page.

Saturday, January 23, 2016

Book Review: The Complete Sherlock Holmes

The Complete Sherlock Holmes, Volume I and Volume II

Sir Arthur Conan Doyle

Introduction and Notes by Kyle Freeman

Softcover, 709 pp. and 709 pp.

Barnes & Noble Classics, 2003

These Barnes & Noble Classics editions of Sherlock Holmes are authoritative, affordable, and printed in good-quality format with few typographical errors. Mr. Freeman's editorial contributions include a couple of enthusiastic and informative introductions, a detailed timeline, and a number of textual notes; all this adds significantly to the book's value. If you want a complete edition of Sherlock Holmes, then these two volumes will serve you well.

Some of the tales collected here aren't worth reading nowadays (I'll give details below), but much of The Complete Sherlock Holmes is still first-rate detective fiction. As soon as I finished The Complete Sherlock Holmes, I added Conan Doyle and his works to my continually updated list of favorite genre fiction.

The Sherlock Holmes tales have certain conventions and repetitive features, which might be tedious for some readers. However, these Holmesian and Watsonian hallmarks are effected differently from story to story, and having all of the stories next to one another also reveals variety within the genre: there are examples here of the puzzle story, the diplomatic intrigue, the urban crime story, and the Gothic horror tale. Some of my favorites, in chronological order:

A Scandal in Bohemiathe story with Irene Adler
The Adventure of the Speckled Banda tale of the macabre
Silver Blaze
The Musgrave Ritual
The Reigate Puzzle
The Naval Treaty
The Final ProblemHolmes dies...or does he?
The Hound of the Baskervilles (novella)atmospheric adventure on the moors
The Adventure of the Empty HouseSherlock Holmes returns!
The Adventure of the Priory School
The Adventure of the Second Stain
The Adventure of the Bruce-Partington Plans
The Adventure of the Lion's Mane

On this website you can see how Holmes aficionados rank the stories. And here is Sir Arthur Conan Doyle naming his own favorites.

  • Most of the stories in the 1927 collection The Case Book of Sherlock Holmes
  • Study in Scarlet (novella) 
  • The Sign of Four (novella) 
  • Valley of Fear (novella)
Fans of Sherlock Holmes usually rate Study in Scarlet and The Sign of Four more highly, but I found the former work immature and the latter work convoluted and overlong. For that matter, I assume that a single Holmes novella is all the average reader really wants to invest in, and in that case there's no question that the novella you want is the Gothically delicious Hound of the Baskervilles.

Monday, January 18, 2016

Kid Cryptograms

As a Christmas present, my kids bought me The Complete Sherlock Holmes, Volume I and Volume II. Inspired by the stories, I created some cryptograms for my kids to play with over the weekend.

The first cryptogram was a book cipher, which was clearly a hit!

To decode a book cipher, you first have to know what book to use. So I included a cartoon showing two of our bookshelves, along with enough information to identify the book to be used for decoding (it was The Wind in the Willows). Now, with the right book in hand, turn to each indicated page number and write down the word that is reached by counting the indicated number of words from the top of the page.

The second cryptogram was based on hidden words. To set the stage for the game, I hid a toy monster somewhere in the house, along with two quarters. Then I created an encrypted message; when decoded, the message reads as if the monster were asking for help. To allow for two players, I divided the cryptogram into two parts, one consisting of the odd-numbered words and the other consisting of the even-numbered words. It looked like this:

To decode the message, replace each word with a word that hides inside it. (For example, replace the word STAVE with the word SAVE.) Then bring the two halves of the message together to reveal the monster's plea for help—and its location in the house.

Sunday, January 10, 2016

Freudenthal's Impossible Problem

An email from a friend arrived just as I was cramming myself into a middle seat for a cross-country flight:

I am thinking of two whole numbers greater than 1 whose sum is less than 100. I tell this to Jason and Brendan, and give Jason the product and Brendan the sum.

Jason: I don't know what the two numbers are.
Brendan: I knew Jason wouldn't know what the two numbers are.
Jason: Ah, now I know what the two numbers are.
Brendan: Ah, now I know what they are as well.

What are the two numbers? Assume Jason and Brendan are perfectly logical, honest, smart, etc.

Talk about good timing! The hours of the flight passed quickly as I scribbled figures in my notebook. (I had the answer by the time we landed, but it was not easy.)

This beautiful puzzle is justly famous; you can read about it online by searching 'Freudenthal's Impossible Problem.'

Saturday, January 2, 2016

How I See Addition Facts

Since I've been doing Saturday School with my kids, I've continued to appreciate how intricate is the structure of the addition facts as they play out in the curriculum. Right now, my younger is learning some of the facts from memory and, for some others, learning the strategy of making ten.

At this stage of learning, making ten is a great strategy for a problem like 8 + 5. But the strategy doesn't help you in a problem like 12 + 3. To solve that problem, at this stage of learning, I'd say you want to

  • appreciate the place value structure as 10 + 2 + 3,
  • know from memory that 2 + 3 = 5, and also
  • understand the meaning of teen numbers so that 10 + 5 = 15.

And in general, each region of the a + b map has its own story. This graphic shows the map with different regions color-coded.

Here is a key to the colors:

I use this map to orient myself toward my kids' learning as they progress toward fluency with addition facts and knowing them from memory. For example, the image below shows the worksheet I made for today's Saturday School. (Downloadable PDF here.) You'll see that the worksheet has 36 sums for practice—precisely the 36 sums that are coded yellow above. This is an intense practice day for making ten. Over the past few Saturdays, we established that the partners of 10 (magenta) were down cold, that there was fluency within 10 (red), and that the structure of the teen numbers was well understood (green). These are the key prerequisites for making ten. (Another is the ability to use properties of addition where helpful.)

Previous posts about Saturday School: 1, 2