Cheryl's Birthday and Other Trick Maths Questions

So this went viral this week.

I hate these things. But I buckled down (at work!) and did it in 15 minutes. It helped to draw the dates as a matrix: months on the top, dates down the side.

The press spin is that 15 year-old kids in Singapore are smarter than almost everyone in the Western world. The excellence of Singaporean secondary education is a common trope of the western press, closely followed by the superiority of Chinese, Japanese and Korean secondary education.

Of course this is nonsense. For one thing, this superannuated grey-haired Anglo did it in about fifteen minutes. (I usually do the “Can you answer these GCSE questions” quizzes and I always ace them in a very short time though not after a couple of mis-steps along the way. The day I can’t ace them is the day I will apply for a job in product development.) For another, the exam board itself stated that this question was to help identify the better students.

And for another, this isn’t a serious question. It’s a trick. It’s the kind of trick question that a certain kind of epistemologist likes to use to discuss abstruse issues, and it’s the epistemological analogue of the trolley problem.

What makes a problem a mere trick instead of an interesting problem? An interesting problem gives rise to some theory to solve it: anything from an algorithm to a 400-page mathematical paper full of abstruse theorems. A trick is solved by a non-transferrable, non-generalisable argument. Remember all those integrals you had to solve at school? You had to play guess-the-substitution that would turn them into simple ones. Finding substitutions is a a trick. Integration by parts is a method, even if it does involve some trial-and-error.

Tricks give people the wrong idea about what a subject is about. The maths A-level syllabus used to be strong on tricks, whereas real mathematics is mostly about geometric insight to suggest theorems, and algebraic slog to prove them. Not finding a transformation or algebraic manipulation that magically makes the answer appear. Ask a serious chess-player whether they do chess puzzles: most of them don’t.

But the general public likes tricks. It likes to think that maths, or chess, or anything else that requires lots of reading, understanding, and actual insight, not to mention lots of trial and error, is really about seeing-something-that-makes-it-easy. Because that makes it magic, and the general public don’t mind not being able to do magic. Magic is, after all, just tricks. But if it’s hard work, and guessing and learning from mistakes, and adapting techniques you read about in some other contexts (that means reading, right?), then we’re looking at choices of how they spent as an adolescent, and now spend as an adult, their time and energy.

And guess what? Most people made choices that means they can’t solve a problem that bright 15-year olds in Singapore can solve.

Peeled Potatoes, The City

First thing in the morning, outside the pub. That's where all those rostis come from.

18 Rules About Scientific Theories and Other Claims By Scientists

Rule 1: Any scientific theory that resembles a Biblical myth, or any creation myth from any other culture or religion, can be rejected without further examination.

Rule 2: Anyone who claims that scientific theories have immediate consequences for social, moral or political policy has to remain silent until they have read Hume’s Treatise on Human Nature and understood why they are wrong.

Rule 3: Any explanation of current behaviour in terms of how human beings lived twenty thousand, or any other number of, years ago, can be replaced by a better explanation referring entirely to the current economic and material circumstances and personal goals of the people involved.

Rule 4: Any scientist who claims their theory shows that people do not have freedom of choice certainly doesn’t understand what freedom is, and probably doesn’t understand their own theory.

Rule 5: Any scientist who claims their theory shows that people are not conscious beings certainly doesn’t know what consciousness is, and probably doesn’t understand their own theory.

Rule 6: Any scientist who claims that their theory should be accepted because “everyone agrees” doesn’t understand what science is.

Rule 7: Anybody who refuses to specify the circumstances under which they would change their theories, beliefs or policies can leave the room now. This discussion is for practical grown-ups. (“Until a better one comes along” does not count.)

Rule 8: Any scientific explanation that blames the subject or patient can be rejected without further examination.

Rule 9: Any theory that only explains the past, and cannot predict the future, is a fact-based creation myth, not a scientific theory.

Rule 10: Any study paid for by an organisation should be accepted only if its conclusions are contrary to the interests of that organisation.

Rule 11: Any regularity, correlation or pattern discovered by number-crunching or statistical techniques should be treated as a curiosity until it is explained by some specific technology or institutional rules.

Rule 12: Any finding from a large-scale survey of people will always confuse cause and effect in such a way as to re-inforce the current social prejudices about those people.

Rule 13: Anyone who says “the plural of anecdote is not data” either doesn’t understand what the word “plural” means, or is trying to sell you their research services.

Rule 14: If the statistics say that 20% of the population do something, and you don’t know anyone who does, it’s not 20% of the whole population, it’s 100% of a smaller chunk of the population that nobody wants to identify out loud.

Rule 15: The source academic paper never says what the press release says it said. Unless it’s a sponsored study, when the academic paper says what the press release needed to say.

Rule 16: Anyone who doesn’t understand the various Quantum theories probably doesn’t understand what a Lie Algebra is. Fix that, and Quantum theories will suddenly become simple.

Rule 17: Anyone who says “logic dictates” doesn’t know that logic doesn’t dictate anything. It doesn’t even tell you how to draw conclusions from what you’ve just dictated. It just tells you how not to screw up drawing those conclusions.

Rule 18: Any popularisation of a scientific theory will distort and simplify the most important features of the theory in direct proportion to the intended sales of the book.

February / March 2015 Review

Cold. More cold. And more cold yet. I think I have worn my faithful Tyrwhitt grey houndstooth coat for four months straight now.

I read Hegel’s Philosophy of Mind, finished Heidegger’s Poetry, Language and Thought, Nevile Shute’s The Trustee from the Toolroom, Max Tegmark’s Our Mathematical Universe, William Byers’ How Mathematicians Think, Patricia Berman's In Another Light: Danish Painting in the Nineteenth Century, Howard Bloom’s The Lucifer Principle, Ian Fleming’s For Your Eyes Only, and Mark Lawrence's The King of Thorns. I think I read the Fleming when I was about eleven, and it clearly formed many of my opinions about Life, The Universe and Everything. I made a start on John Eliot Gardiner's book on J S Bach, and that's going to be read in several instalments this year.

I watched Inherent Vice, Hinterland, Appropriate Behaviour at the Curzon Soho; went with Sis and Mother to the Sargent exhibition at the NPL; had a Moroccan in Shepherds Market with Sis in February and fish at Kensington Place in March. We liked Kensington Place. On DVD I watched my way through the BBC’s Strangers and Brothers, The Event, and S1 of The Bridge.

I changed my work-outs to include 12-15 sets of 5 pull-ups with pyramiding supports: starting at 57 kgs (I weigh 97 *cough*) and dropping down to 50, 43, 36, 30, then going back up to 57 and back down to 43. Everything else I do is subordinate to that. I’m going to adding in some lat pull-downs, and may try the thing where you jump up to the bar and then let yourself down slowly. I did that once for a few reps: it ached for days afterwards.

Finally I got the beginning and end of my interminable Riemann-Roch essay sorted out, and now only have some stuff about Riemann surfaces to finish it off.

Then at the end of March I left a couple of pairs of trousers on the morning train that I had been intending to take for dry cleaning while I was on a planned six-day Easter break, which is passing with a seating, fever-y, nose-stuffing, cough-retching, sleep-depriving cold.

God hates me.

The Load Must Be Uniformly Distributed Between Hoppers

Fire Drill, Bishopsgate

Every day one or other of the office blocks in the City tips its occupants onto the streets. Companies with trading floors leave a couple of traders inside unless they know it's real fire and not a drill or some over-sensitive alarm. Then it takes about twenty minutes or so to get everyone back in and up to their floors.

(I know: I cheated the dates. The last weekend was weird and this week more so, involving cough and fever.)

Ten Dumb... err Clever Programmer Interview Questions

Over at The Simple Programmer (I think), they posted a bunch of questions that recruiters ask programmers and analysts. Here are my answers.

1. "What would you do if you were the one survivor in a plane crash?" (Airbnb Trust and Safety Investigator job candidate). More Airbnb interview questions. ME: where did it crash? What that tells you: Like everyone with a tonne of experience, I know context is all.

2. "What's your favorite 90s jam?” (Squarespace Customer Care job candidate) ME: Jam as in music or jam as in basketball or jam as in jelly? What this tells you: You come at me with ambiguities, and I’m going to help you clarify them.

3. "If you woke up and had 2,000 unread emails and could only answer 300 of them, how would you choose which ones to answer?" (Dropbox Rotation Program job candidate.) ME: In descending order of the ability of a non-response to get me fired. What this tells you: I’m political

4. "How many people flew out of Chicago last year?" - (Redbox Software Engineer II job candidate ). ME: This is one of those Fermi estimation questions isn’t it? Actually, I’d probably look up the answer on Wikipedia. What this tells you: I know where to look up information.

5. "How much do you charge to wash every window in Seattle?" (Facebook Online Sales Operations job candidate). ME: Well, what you want me to do is a Fermi estimation. Or are you looking to see how much I really want as a salary? What this tells you: I think you’re playing games.

6. "Given 25 swimmers and a pool with five lanes, what is the minimum number of heats needed to determine the three fastest swimmers in the group?" (CKM Advisors Data Scientist job candidate.) ME: Oh heck. You didn’t say this was a combinatorics job. Not my strength. Nice meeting you. What this tells you: I’m not your guy.

7. "If you were a Muppet, which would you be?" (TicketNetwork Executive Support job candidate.) ME: Mal Reynolds in Firefly. What this tells you: I understand what you’re getting at with this question, so here’s an answer I can live with.

8. "How many gas stations are there in America?" (Zappos Family Senior Financial Analyst job candidate.) ME: What is it with Fermi estimation questions? Call Exxon. Ask them.

9. "You have a 1 mile long x 1 mile wide private island that you wish to turn into a resort. A plane requires a 2-mile long runway to take off. What do you do?" (Riot Games QA Analyst job candidate) ME: You want me to build a circular runway, don’t you? it would be just over 3 miles long. It wouldn’t work though because the airplane tyres and undercarriage wouldn’t take the centrifugal force at anything near take-off speed, not to mention the awful airflow wouldn’t generate enough lift.

10. "Why is the earth round?" (Twitter Software Engineer job candidate) ME: it isn’t. It’s oblate. And it’s oblate because gravity, centrifugal force and liquid core. Or something. What this tells you: I don’t do groupthink assumptions.

I know. I’m not going to get the job. But then, if they’re asking these questions, I don’t want it.