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.


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 


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."


Where Boys Outperform Girls in Math

Stanford study of some 260 million test scores shows that boys doing better than girls in math is related to their being in a rich, white, and suburban district. In poor and black districts, girls tend to do better than boys. This is distinct from English proficiency, which is constant across all these factors (girls always outperforming boys there):
The study included test scores from the 2008 to 2014 school years for 10,000 of the roughly 12,000 school districts in the United States. In no district do boys, on average, do as well or better than girls in English and language arts. In the average district, girls perform about three-quarters of a grade level ahead of boys.
But in math, there is nearly no gender gap, on average. Girls perform slightly better than boys in about a quarter of districts – particularly those that are predominantly African-American and low-income. Boys do slightly better in the rest – and much better in high-income and mostly white or Asian-American districts.
Note that this is synchronous with gender roles of parents in the given districts. In rich, white, suburban districts, parents are more willing to say they have egalitarian values, but actually more like to have traditional gender roles in the family (e.g., full-time working father and stay-at-home mother).

New York Times.


How to Document a Series of Button Clicks

Note to self: When documenting a series of interface button clicks for readers to follow, consider the following survey (in order of company sales/size in 2018):

In summary, I should (keep) using angle-brackets, as do the biggest 3 tech companies, instead of some other option.


17th Century Science Ciphers

Did you know? It was common in the 17th Century for scientists to publish cipher-versions of early findings, so as to establish priority in the discovery. (Something of an early, public-encrypted arXiv, as it were.) Huygens wrote in 1668:
a way of securing his discoveries and inventions for the future by way of cypher or anagram, to be lodged in the Register-book of the society, till he should think it convenient to explain them in a common language; making withal a beginning of this way of communicating new discoveries by sending the following cypher; which was ordered to be entered into the Register-book.

Stack Exchange: Skeptics.


Oxford: Likely Alone in Universe

A new assessment from Oxford University finds it quite likely that humans are alone in the universe:
Our main result is to show that proper treatment of scientific uncertainties dissolves the Fermi paradox by showing that it is not at all unlikely ex ante for us to be alone in the Milky Way, or in the observable universe.

Our second result is to show that, taking account of observational bounds on the prevalence of other civilizations, our updated probabilities suggest that there is a substantial probability that we are alone.


Gates Foundation Considered Harmful

Independent assessment of the Gates Foundation's intervention in the last decade, to the tune of $575 million, shows it not just to be wasteful, but even actively damaging:
Laudable as the intention may have been, it didn’t work. As the independent assessment, produced by the Rand Corporation, put it: “The initiative did not achieve its goals for student achievement or graduation,” particularly for low-income minority students. The report, however, stops short of drawing what I see as the more important conclusion: The approach that the Gates program epitomizes has actually done damage. It has unfairly ruined careers, driving teachers out of the profession amid a nationwide shortage. And its flawed use of metrics has undermined science.

Cathy O'Neil at Bloomberg.


Growth Mindset Found Lacking

Large-scale meta-study at Michigan State finds that the "growth mindset" intervention that's been all the rage for the last few years doesn't actually accomplish much:
"This research is important because millions of dollars have been spent on growth mindset interventions in schools," said Alex Burgoyne, a Ph.D. student studying cognition and cognitive neuroscience. "Our results show that the academic benefits of these interventions have been largely overstated. For example, there was little to no effect of mindset interventions on academic achievement for typical students, or for other groups who some have claimed benefit substantially from these interventions, including students facing situational challenges, such as transitioning to a new school."
Medical Xpress.


Illustration of Platonic Solids

A very nice illustration of why there are only 5 regular polyhedra (Platonic solids), by Martin Holtham on Twitter:


Stop Grading on a Curve in New York Times

By Adam Grant in The New York Times, two years ago:
The more important argument against grade curves is that they create an atmosphere that’s toxic by pitting students against one another. At best, it creates a hypercompetitive culture, and at worst, it sends students the message that the world is a zero-sum game: Your success means my failure.
The New York Times


Animal Numerosity Everywhere

The NY Times reports on a themed issue of the Philosophical Transactions of the Royal Society B, in that many animals have impressive built-in numerosity ability: being able to distinguish between quantities between one and five, say, or proportionally in how 25 is different than 30. In some cases, better than humans: monkeys can visually identify certain number sequences in a split-second.

We are reminded of when Noam Chomsky conjectured that enumeration might be the first mental stepping stone on the way to language -- or how apt it is that we call the "natural numbers" by that name.
Scientists have found that animals across the evolutionary spectrum have a keen sense of quantity, able to distinguish not just bigger from smaller or more from less, but two from four, four from ten, forty from sixty.

Orb-weaving spiders, for example, keep a tally of how many silk-wrapped prey items are stashed in the “larder” segment of their web. When scientists experimentally remove the cache, the spiders will spend time searching for the stolen goods in proportion to how many separate items had been taken, rather than how big the total prey mass might have been.

Small fish benefit from living in schools, and the more numerous the group, the statistically better a fish’s odds of escaping predation. As a result, many shoaling fish are excellent appraisers of relative head counts.

Guppies, for example, have a so-called contrast ratio of .8, which means they can distinguish at a glance between four guppies and five, or eight guppies and ten, and if given the chance will swim toward the slightly fishier crowd.

Three-spined sticklebacks are more discriminating still: with a contrast ratio of .86, they’re able to tell six fellow fish from seven, or 18 from 21 — a comparative power that many birds, mammals and even humans might find hard to beat.

New York Times.


Is Accepting Math Deficiency Destroying Journalism?

From 2013, an article by a professional journalist, who thankfully skipped any math in college -- then when he went for an MBA to understand the business he was in, discovered that calculus was a prerequisite for entry. So he committed to the road from lowest-level K-6 remediation up to calculus.

He points out that being "bad at math" is so accepted in the journalism industry, that it's actually a point of pride. We recall the article in the New Yorker three years ago this month about Yitang Zhang's marvelous progress on the twin primes conjecture, in which the journalist actually framed the entire story around how he knew so little math, he had to lie and cheat his way through high school algebra.

In our current case, the journalist (and now professor) suggests that this anti-math bias in journalism may actually be a contributing factor to the collapse of the industry -- in that both (a) the present cohort is unable to make sense of quantitative, scientific, or technological stories, which grow ever more essential to the world around us; and (b) they are unable to understand the financial and business case of their industry.

Well, Professors Kimball and Smith, welcome to journalism, where “bad at math” isn’t just a destructive idea — it’s a badge of honor. It’s your admission to the club. It’s woven into the very fabric of identity as a journalist.

And it’s a destructive lie. One I would say most journalists believe. It’s a lie that may well be a lurking variable in the death of journalism’s institutions. 

Name me a hot growth area in journalism and I’ll show you an area in desperate need of people who can do a bit of math. Data. Programming. Visualization. It’s telling that most of the effort now is around recruiting people from outside journalism to do these things. 

But it doesn’t end there. Name me a place where journalism needs help, and I’ll show you more places where math is a daily need: analytics, product development, market analysis. All “business side” jobs, right? Not anymore. 

Truth is, “bad at math” was never a good thing in journalism, even when things like data and analytics weren’t a part of the job. Covering a city budget? It’s shameful how many newsroom creatures can’t calculate percent change. Covering sports? It’s embarrassing how many sports writers dismiss the gigantic leaps forward in data analysis in all sports as “nerd stuff.”

In short, we’ve created a culture where ignorance of a subject is not only accepted, it’s glorified. Ha ha! Journalists are bad at math! Fire is hot and water is wet too!

Nieman Lab.


Ontario Elementary Teachers Need Remedial Math

A story from 2016 on how in-service elementary-school teachers in Ontario are only about 50% likely to know K-6 math skills such as fractions or percentage calculations. In response, supplementary remedial courses are delivered for these instructors:
Teachers’ math phobia, which faculties of education across North America view as a “huge problem,” are seen as one factor in Ontario’s falling student math scores, especially in grade school, where most teachers have a liberal-arts background and have not studied math since high school...

Some professors say student teachers are often in tears when they try to recall their grade-school math, and tell them they’re grateful for the emergency crash courses.

“I’ve got some mathematically brilliant teacher candidates, but I’m also working with some who don’t know how to multiply or divide,” noted professor Mary Reid of U of T’s Ontario Institute for Studies in Education (OISE). “They have no idea what a ‘remainder’ is. They think a remainder of 3 is the same as decimal 3.”
The Star


Facebook's New Unit of Time

Thesis: People who think every unit needs to be a power of 10 don't understand the importance of proper divisors.

Case study: Engineers at Facebook just invented a new unit for synchronizing video frames, called a "Flick", which -- to avoid rounding errors with floating-point math -- needs to be evenly divisible into any of the common video frequencies: 24hz, 25hz, 30hz, 48hz, 50hz, 60hz, 90hz, 100hz, or 120hz. And also multiples of those by 1,000. And also common audio sampling rates like: 8kHz, 16kHz, 22.05kHz, 24kHz, 32kHz, 44.1kHz, 48kHz, 88.2kHz, 96kHz, and 192kHz. Since the least common multiple (LCM) of all those numbers is 705,600,000 (see: Wolfram Alphalink) the "Flick" is therefore defined as 1/705600000 of a second.


Yes, Scantrons Still Require a Pencil


Do Scantron machines still require that the forms be filled out in pencil? You'll find many sites online that claim the answer to be "no", that was only truly a requirement some decades ago, and that one should feel free today to use any dark pen ink (example). However, with a colleague at my college I've recently tested this (December, 2017) on two different recent models of Scantron machines, and found that black ink is entirely not seen by either machine (all such answers scored as if blank/incorrect). So from the evidence at hand, the answer seems to be "Yes, Scantrons still require a pencil".


A standard Scantron answer sheet was filled out in pencil, with three questions marked. A student response form was filled out using a black felt-tip PaperMate Flair pen (link), with two questions marked correctly and one answer incorrectly. See forms below.

Scantron forms; sample student response in black ink on the right.

These were run through two separate machines available at our college: a Scantron 888P+ and a Scantron Score. Both systems are identified as using OMR (Optical Mark Recognition), which several online sites claim should work identically for pencil and ink. I've been unable to find exact dates of production, but the Scantron Score is a newer model. The 888P+ has been installed at our college for at least 12 years; the Score was installed more recently, I think some time after 2010. Both models tested are shown below.

Scantron 888P+

Scantron Score


On both Scantron machines, the sample student form in ink was marked with all submitted answers wrong, the same as if every entry was blank. See the image of the forms above, with the sample response for graded on the right. Every question has a letter to the right, indicating correction of an incorrect student response; the total score in the bottom-right is 000 (zero) for both models. (This form is double-marked after being run through the two machines; 888P+ markings are in red, while Score markings are black.)


Scantron OMR machines, even fairly modern ones in the last few years (as of 2017), fail to recognize marks with blank ink all of the times we tested it, across two different models. Instructors should continue insisting that students bring pencils to tests graded with Scantron machines, and make sure to not advise students that ink pens will work the same way.