Monday, April 29, 2019

Solitaire: Chance for Starting Duplicates

In Klondike Solitaire, what's the chance for starting with two face-up cards of the same rank & color (what we might call "shadows", cards which don't help us very much)?

There are 7 face-up cards in starting Solitaire, so we consider the ways to choose 7 cards randomly without any duplicates. Every time we select such a card, the number available for the next draw (avoiding "shadows") goes down by 2, while the cards in the total deck goes down by 1. Therefore the chance for no-shadows is:
$${52 \over 52} \times {50 \over 51} \times {48 \over 50} \times {46 \over 49} \times {44 \over 48} \times {42 \over 47} \times {40 \over 46} \approx 0.63$$
This in turn means that the complement event, i.e., getting any shadows at all (at least two cards with duplicate rank & color), has a probability of:
$$1 - 0.63 = 0.37 = 37 \%$$
That is: About one chance in three.

More about Solitaire. 

Monday, April 22, 2019

Facebook Learning Debacle

Yesterday, the New York times published an expose on how schools in certain (poor, rural) places are being used as guinea pigs and getting "Zucked" by the Facebook founder's "Summit Learning" initiative, yet another plan to replace teachers with computer time. The highlights are sad and predictable:
  •  A program that promises "personalized learning" at each student's individual pace. Software free of cost, but school district must buy everyone a laptop.
  • Also, Facebook/Summit collects reams of information on the students involved, and expects to keep tracking students through college and beyond. 
  • The program was built by a grand total of 5 Facebook engineers (mo information on whether they have any training in education or pedagogy issues). 
  • A spokesperson says it is based on, "building a curriculum from the open internet", that is, mostly links to outside web sites. Examples given include links to the Daily Mail tabloid and Christian conversion therapy sites.
  • The program "asks schools to commit to having students meet weekly in person with teachers for at least 10 minutes", but reports say not even this is happening.
Students are reporting high levels of anxiety, eye strain, hand cramps, and even seizures. Said one parent who visited a classroom, “We’re allowing the computers to teach and the kids all looked like zombies”. Some places are seeing pushback like student protests, walkouts, and parent removing their children from schools.

One reminder from yours truly: the promise of "personalized learning" is not new. It's been around at least since multimedia in the 90's, or the PLATO computer system in the 60's, or correspondence courses in the 40's, or the Gutenberg printing press, depending on how you count such things. None of them have come close to denting the need for real human teachers.

Monday, February 11, 2019

Honeybee Addition and Subtraction

Researchers in Australia and France claim to show honeybees learning to do symbolic addition and subtraction (really just incrementing and decrementing) based on 1-5 colored shapes at a time. Interesting ramifications if that's true.


Many animals understand numbers at a basic level for use in essential tasks such as foraging, shoaling, and resource management. However, complex arithmetic operations, such as addition and subtraction, using symbols and/or labeling have only been demonstrated in a limited number of nonhuman vertebrates. We show that honeybees, with a miniature brain, can learn to use blue and yellow as symbolic representations for addition or subtraction. In a free-flying environment, individual bees used this information to solve unfamiliar problems involving adding or subtracting one element from a group of elements. This display of numerosity requires bees to acquire long-term rules and use short-term working memory. Given that honeybees and humans are separated by over 400 million years of evolution, our findings suggest that advanced numerical cognition may be more accessible to nonhuman animals than previously suspected.

Monday, January 21, 2019

Computer-Based Naval Training Failures

A fascinating article by a PhD candidate in military history: On the U.S. Navy's switch from face-to-face classrooms for training officers in surface warfare combat to independent computer-based training (CBT) aboard one's ship from 2003 - 2012 -- which turned out to be both a training disaster and also wildly inequitable, and was replaced with renewed face-to-face training after that time.

For me, this seems to echo the recurrent drumbeat of hopes for distance/computerized classwork saving time and money, turning out to be generally complete failures, but administrators for various reasons eternally refusing to face up to the facts and evidence (out of an abundance of vain hopes). At least here we have a case study of an institution that has some higher motivation for responding to the failure, in that people's lives and billions of dollars in equipment are immediately at risk from obviously poor training. A key quote, I think, and more widely applicable:
Finally, changes undertaken with the principal goal of saving money or hurrying a process are fraught with danger. The overriding pressure to achieve financial or time savings threatens to overtake innovative ideas and turn them into quick-fix vehicles for the achievement of specific goals. 

(Coincidentally, my gaming blog today has a link to some excellent documentation on the history of wargaming used to train officers in the U.S. Navy: see here.)

Monday, December 17, 2018

NY Times Magazine Finds C.I.'s Baffling

Another journalist publicly declares their inability to understand the most basic math: in this case, confidence intervals. This is Statistics 101, people.
When I asked that representative to check with a supervisor, she did, then returned to tell me that the company’s certainty was 99.7 percent. Those answers were confusing, because behind each of Johnson’s percentages was a range from which each ancestry point was drawn. For example, when we clicked on Johnson’s Benin/Togo segment, which had been assigned 10 percent of her ancestry, the site showed that the percentage of her DNA from those nations could be as low as zero and as high as 21. In fact, every one of her African links showed a range that started with zero, while her Europe South’s percent had a range of 9 to 33. Even the customer-service representative agreed that it was hard to fathom that the company could be so certain about the percentage when the range behind it ran to zero, which it did in four of the six geographic findings on Johnson’s report. 

New York Times Magazine.

Monday, September 10, 2018

Why Do Nigerian Scammers Say They Are From Nigeria?

From 2012:
Far-fetched tales of West African riches strike most as comical. Our analysis suggests that is an advantage to the attacker, not a disadvantage. Since his attack has a low density of victims the Nigerian scammer has an over-riding need to reduce false positives. By sending an email that repels all but the most gullible the scammer gets the most promising marks to self-select, and tilts the true to false positive ratio in his favor.

Microsoft Research 

Monday, September 3, 2018

Dale Carnegie on Times Tables

Here's an excerpt from Dale Carnegie's uber-famous book, How to Win Friends and Influence People (Part 4, Section 8):
Clarence M. Jones, one of the instructors of our course in Cincinnati, Ohio, told how encouragement and making faults seem easy to correct completely changed the life of his son.

"In 1970 my son David, who was then fifteen years old, came to live with me in Cincinnati. He had led a rough life. In 1958 his head was cut open in a car accident, leaving a very bad scar on his forehead. In 1960 his mother and I were divorced and he moved to Dallas, Texas, with his mother. Until he was fifteen he had spent most of his school years in special classes for slow learners in the Dallas school system. Possibly because of the scar, school administrators had decided he was brain-injured and could not function at a normal level. He was two years behind his age group, so he was only in the seventh grade. Yet he did not know his multiplication tables, added on his fingers and could barely read.

"There was one positive point. He loved to work on radio and TV sets. He wanted to become a TV technician. I encouraged this and pointed out that he needed math to qualify for the training. I decided to help him become proficient in this subject. We obtained four sets of flash cards: multiplication, division, addition and subtraction. As we went through the cards, we put the correct answers in a discard stack. When David missed one, I gave him the correct answer and then put the card in the repeat stack until there were no cards left. I made a big deal out of each card he got right, particularly if he had missed it previously. Each night we would go through the repeat stack until there were no cards left.

Each night we timed the exercise with a stop watch. I promised him that when he could get all the cards correct in eight minutes with no incorrect answers, we would quit doing it every night. This seemed an impossible goal to David. The first night it took 52 minutes, the second night, 48, then 45, 44, 41 then under 40 minutes. We celebrated each reduction. I'd call in my wife, and we would both hug him and we'd all dance a jig. At the end of the month he was doing all the cards perfectly in less than eight minutes. When he made a small improvement he would ask to do it again. He had made the fantastic discovery that learning was easy and fun.

"Naturally his grades in algebra took a jump. It is amazing how much easier algebra is when you can multiply. He astonished himself by bringing home a B in math. That had never happened before. Other changes came with almost unbelievable rapidity. His reading improved rapidly, and he began to use his natural talents in drawing. Later in the school year his science teacher assigned him to develop an exhibit. He chose to develop a highly complex series of models to demonstrate the effect of levers. It required skill not only in drawing and model making but in applied mathematics. The exhibit took first prize in his school's science fair and was entered in the city competition and won third prize for the entire city of Cincinnati.

"That did it. Here was a kid who had flunked two grades, who had been told he was 'brain-damaged,' who had been called 'Frankenstein' by his classmates and told his brains must have leaked out of the cut on his head. Suddenly he discovered he could really learn and accomplish things. The result? From the last quarter of the eighth grade all the way through high school, he never failed to make the honor roll; in high school he was elected to the national honor society. Once he found learning was easy, his whole life changed."