Dumbing-Down GCSE Maths - Again?

The Guardian had another "tough maths question" on Friday, to accompany an article about how the GCSE exam boards were being asked to dumb-down make the exam accessible to pupils of all abilities. We’ll pass that one over, because the fact the request was leaked means that even the exam boards think it’s ridiculous.

So here’s the question:

And here’s the answer:

Angle TAP is a right angle, because PTN is an equilateral triangle (all sides equal) and it’s half-way along, so bisects the angle at P and must do so perpendicularly. OP can be calculated from Pythagorus (sqrt(90^2 – 40^2) = 80.62. AT is 20cm long and is the hypotenuse of a right triangle ATP, so AP = sqrt(40^2 – 20^2) = 30.64. We know OP and AP and tan(OAP) = OP/AP = 2.327 and angle OAP = arctan(2.327) = 1.165 radians = 66.75 degrees.

The question is two applications of Pythagorus’ theorem, one of SOHCAHTOA and one of the properties of equilateral triangles. The question points towards the solution by a) asking you to calculate angle TAP and then calculating AP. In the context of GCSE maths, you can only calculate AP if angle TAP is a right-angle. They don’t do the general version of Pythagorus. That’s a clue right there.

What makes it difficult is that the prompts in the question only take you half-way there. To get angle OAP, you need its sin, cos or tan, and you can’t read those off from the question. Because OA is not as long as ON. (Following the hint that TON is an isosceles triangle will take you up the garden path.) We know AP so we need OA or OP. OPT is a right triangle with two known lengths (PT and OT), so we calculate OP. This gives us the Opposite and the Adjacent of angle OAP, and that’s its tangent. Now find the arctan on your calculator.

It’s the need for sustained reasoning, for spotting the false starts, and for solving the problem of the missing bit of information, that makes this a difficult question. It’s not the maths that’s hard - this is Year 8 at most - but the ability to perform sustained reasoning and problem-solving.

Most people can’t do that, anymore than most people can run five-minute miles or deadlift 200+ lbs. So there’s two things here: the first is to sort out the young people who show some aptitude for it, so they can pointed to subjects where it is needed; the second is how to design a syllabus and examination that gives the rest of the world something useful. Even if you can’t deadlift 200lbs (I can’t) you can still be taught useful exercises. Even if you can’t conduct a chain of reasoning, you can still be taught to do basic numeracy, estimation, ratios and comparisons.

My memory is that, one year after doing O-level maths, and so half-way through an OND in engineering, I and everybody else on the course looked at an O-level paper and realised it was trivial compared to what we had learned since. How had we ever thought it was hard? That was when the O-level included calculus, and most of us knew about “imaginary numbers” and had done ever since learning the formula for solving a quadratic equation. Back then the maths teachers used to say they thought that including complex arithmetic in the O-level was only a couple of years away. Well, we’re regressed a lot since then.

ZOUT - Zandvoort

Spent the weekend over in the Netherlands, and have been Python-ing again. This was where I went after arriving at Schipol. When I arrived the sky was overcast, but I'm a believer, and within an hour it looked like this.

I like beaches. If only the good ones weren't so darn far away.

61

Is a house-number, not an age. It's a piece of arithmetic based on my date of birth and today's date. I never felt as old as I did when I was over-weight and in a dead-bedroom relationship in my mid-fifties. Then I joined my gym, and after my second boxing class recognised that I could either get my ass kicked, or kick ass. Getting old means you stop kicking ass. Growing older means that kicking ass takes more effort and has longer recovery times.

I don't expect to behave like a thirty-something. I don't have the hormones, I've sorted out the neuroses. I stay in more and do random stuff less. I used to walk in parks on weekend afternoons, but if I do that now, I almost pass out from the histamines from the pollen I get more sensitive to each year. I can go walking in winter, and then it's too cold. I read for intellectual challenge or entertainment: I've done my English Lit duty reading. I've seen Battleship Potemkin and Man With A Movie Camera, so I have no qualms watching Nikita just because Maggie Q. I leave Friday and Saturday nights to the kids, and Saturdays to the parents. I get older, I adjust. That's what smart people do. And me, even if I'm a little slow on the uptake.


If you're an able-bodied man, it is never too late to re-build your body and mind. I've done it twice: in my early-30's and late 50's. I couldn't do reasonable deadlifts (for an office worker) until six months ago. If you've had an education you can always pick up the books again. That's why I can give you a very simple explanation of why the spectrum of a cylinder has trivial higher co-homology, even though the cylinder itself has a non-trivial first group in the usual topology. I know. I wouldn't have understood a word of that ten years ago either.

In a couple of weeks I begin a year or more's worth of orthodonty. And I will after a bit more hesitation get some personal training sessions to change up the work I do in the gym. The trick is not minding that I have to re-build myself. And not minding that my social life is limited to a few good friends, and that my best sexual days are behind me. That's going to happen to you, and you can work with it or let it get you down.

62? Bring it on.

Why Evolution is an Easy Target for Fundamentalists

I read Wolpoff and Caspari’s Race and Evolution recently. It’s an biographical account of the various views about race in evolutionary theory. The overwhelming impression it left was that all those palaeontologists were and still are, making very large generalisations on the bases of very small amounts of highly interpreted evidence. That's a “feature" of the history-of-the-universe-and-mankind theories: just think of the recent BICEP2 hype-to-epic-fail incident.

To invent theories about the development of the human race on the basis of what are, let’s be blunt, a few scattered bits of bone that require years of training to “see” properly, is speculative science of the highest order. Wolpoff and Caspari acknowledge that the origin-of-humans theories that get the publicity are the ones that fit best with the dominant public political and moral views of the time. Hence the popularity of Out-of-Africa theories. Should anyone prove that Black Africans and White Europeans have significant genetic differences (whatever that might mean) they will be told to shut up or find another job. Should a lady biologist prove that the current human race consists of the males of one previous species and the females of another, the massed ranks of lady columnists would be asking why it took science so long to prove what everyone has always known. (It would be impossible for a male biologist to publish such a paper.)

Evolution is a process without a mechanism. I’m quite happy to accept that our present flora and fauna are the result of breeding and some as-yet-to-be-understood feedback mechanism between environment, phenotype and genotype. What is missing is an adequate explanation of the engineering of the DNA molecule.

The usual story of evolution is that it happens very gradually, taking thousands of years to develop even the smallest successful change to the phenotype, like a particularly inept Victorian experimental inventor. But this cannot be right. Complicated things, like knee joints and legs, have to be done entire, at once, or not at all. How does a animal exist with half a knee? Or a ball head for the lower leg but no socket (yet) on the upper leg? Or consider the development of vision. The first species able to see clearly would have such a competitive advantage over the others that it would simply wipe all the others out. It must have developed in all the relevant species at the same time. Or else there must have been a period of many millions years before predator-pray systems developed. And if Nature experiments, where are the six-fingered guitarists? Something seems to be keeping Nature’s experiments on most species within a tight pattern. (In case you think six-fingered guitarists are a silly idea, remember that horses and many other “four-legged” animals are actually “single-fingered” animals.)

When we understand the fine-structure dynamics of the DNA molecule, we will see that, just as there is only one way to design a knee, and a few to design an eyeball, there are only a limited number of ways a DNA molecule can be stably structured. (‘Limited’ meaning ‘a lot smaller than the number of possible chess games’. While the words that can be formed by the DNA alphabet are potentially limitless, all but a couple of million those combinations won’t lead to structurally stable molecules. Or something along those lines.)

An adequate theory of evolution would be based on an understanding of changes in DNA arising from a) sexual combination, b) environmental damage, c) the only-slightly-understood constructive feedback between environment, phenotype and genotype. When we understand how DNA works, the theory of evolution will be replaced by DNA technology and the history of climate, land mass movement, meteor strikes, large-scale volcanic eruptions and other such events. And all those Vulgar Evolutionist Just-So Stories trotted out to explain every little weirdness of animal behaviour or appearance? Consigned to the tactful forgetfulness of history.

So when I said that evolution doesn’t have a mechanism, I bet you said “sexual selection” under your breath.

Darwin suggested two methods: combat (lions, deer, wolves), when the male appoints himself after fighting with other males, and the females go along with it; and display (the peacock) where the one or both sexes attract the other with some bling or show-off tricks. Quite how otters and penguins fit into this is a stretch of anyone’s imagination - doesn’t it have something to do with pebbles?

A species that is able to survive significant changes to its environment, and even the odd forest fire or major earthquake, cannot be fine-tuned to its existing environment, must have a large set of variations in its genotype and a reasonably rapid environment - phenotype - genotype feedback system. (Otherwise, like smallpox, it can be eradicated. Common cold viruses have the variation and adaptation of the Devil.) That means one or both of the genders can’t be overly fussy in what they look for. In combat-selecting species, it would seem to make sense that the females are the major source of variation, and that the male lion lacks discrimination; and in display-selecting species, the variation and lack of discrimination needs to be in both genders. If males display, they have to be prepared to mate with dull-looking females, and vice-versa; if both do, or don’t, display, each has to be prepared to settle for whoever happens to handy at the time.

A robust species doesn’t actually go in for a lot of selection. It can’t, because it needs genetic variety to survive change. Females choose because “he made me laugh” or “I like bald men”, and accommodating pop-evolutionists tell them that both those reasons are excellent markers for evolutionary advantage. Yesterday they told some other women that long hair and a serious demeanour were also excellent markers for evolutionary advantage. The individual selects, but one individual’s turn-on is another’s turn-off. So a species-wide genetic change cannot be propagated by sexual selection, nor can a particular gene be de-selected by it, because there’s always going to be enough males and females who find the change unattractive, or take up the cause of genes that the majority wish would go away. Which is why women don’t all look like Behati Prinsloo and men don’t all look like Jake Gyllenhall.

Nope. Sexual selection is a crock. But that, and random mutations, are all the evolutionists have until they get a proper theory of DNA engineering. No wonder Evolution is such an easy target for fundamentalists.

April 2015 Review

I was ill. One the first day of the month I woke up and knew I shouldn’t leave the front door, less I fall over in the Cineworld car park on my way to the station and lie there unable to move. I had a cough, cold and fever all the way through Easter and the Thursday and Tuesday I took in addition. Monday 30th of March, I brought in two pairs of trousers for cleaning at Jeeves, and left them on the train. Never leave anything in a plastic bag on the trains that go through Richmond from Waterloo: you will never see it again. I even visited Lost Property in the grand tradition of Futile Gestures. I struggled through the two weeks after Easter, and then took a long weekend. When I returned to work, I felt a lot better, but was still moving slowly.

I emerged from that three-week illness and weakness with an understanding that I had let myself get into a rut over the last six months. I didn’t have a bunch of resolutions, but I did write down a number of things I needed to do and stop prevaricating about buying.

I saw exactly one film the whole month: John Wick, at the Cineworld. However, on the box sets, I went through Scandal, Elementary S2, The Bridge S2 and Fringe S1. I also saw a number of the Fake or Fortune programmes on You Tube.

I read Wolpoff and Caspari’s Race and Human Evolution, Ahmet Hamdi Tanpinar’s The Time Regulation Institute, Douglas Coupland’s Kitten Clone, and Philip Mould’s Sleuth.

Sis and I dined at The Providores on Marleybone High Street, and pronounce it excellent. So do the crowds of well-heeled Maylebonians.

I started the Thursday Yoga classes again. This is because I have decided to leave my car at Richmond and take the tube back from time to time. It works well for Yoga as I’m not thinking about rushing back to catch the trains immediately afterwards and the whole thing feels more relaxed. The Yoga itself? Ouch. I weigh a lot, and I cannot “float…into Plankassana”. When I do it, it’s called a press-up. Stop sniggering and knock out ten press-ups now. Thought so… not as easy as it sounds.

Plus the garden got its post-Winter cut. This is not an easy thing to do.

I started wearing a Fitbit Flex again. Was it co-incidence that I also resumed the alternate Waterloo-Holborn walk? I don’t think so. In the week I do 10,000=+ steps every day, but at the weekend, well, it’s Saturday, and I’m only going to put it on this evening to track my sleep. Turns out, I’m restless most nights, and about 15-20 minutes worth. That cuts into one’s beauty sleep. I’m not tracking calories. That might come later.

And it was also Hay Fever month. I pass out on the train on the return journey. Zonk. On the worst days, it really does feel like I’ve been injected with something.

This Post Delayed by a Python

One of the tasks in my sorting-out-the-photos project was putting all the files into directories according to the year-month. I could do this manually, but I turned it into a project involving a Python program. I’ll write about that later. I’ve been doing that, knocking the rust off what I did know and learning a bunch of new stuff. And also being reminded that the majority of the work in a program with a GUI is the GUI, not the core functionality. I’ll be back soon.

A War on Drug Makers, Not Drugs

The Economist had an editorial about drug policy this weekend. The article didn’t like existing policies, and felt that addicts should be treated as victims rather than perpetrators, but held off on what States should do about the perpetrators. Except to have a conference at the UN. That’s because what needs to be done is a little, well, not the sort of thing The Economist wants to be seen suggesting.

The First Rule of Futurology is that genies can’t be put back inside boxes. Which means that the West is stuck with a large-scale drug problem. The reason is that opiate-based, amphetamine-based and hallucinogenic drugs are absurdly cheap and easy to make, have a high value to the ultimate consumer, and therefore offer large and easy profits. If the State legalised these drugs, it would need to license their production and distribution, and it would inevitably tax the product. Those taxes would represent excess profits for criminals who continued to make and supply directly as they do now. To drive the criminals out, the prices would have to be low enough so that only large producers could get the economies of scale needed to reduce the unit costs of production and distribution low enough to still make profits. A tab of ecstasy would need to be priced at around the price of an economy aspirin. And that’s not going to happen.

A rule of any of the substance-recovery 12-Step movements is: “no mood-altering chemicals”. Exceptions can be made for prescriptions made for medical emergencies. The harm to the individual is that the drug prevents, one way of another, them from tackling the problems in their characters that make it hard for them to live contributing and considerate lives. The harm to the people around them is the trouble and drama they cause, and the harm to the taxpayer is the cost of the crime they cause, and the medical services they need and the welfare payments they receive.

Living without mood-altering chemicals, remembering that alcohol is one, requires some behavioural and psychological disciplines that are antithetical to what most people would consider a normal life. Banning all mood-altering chemicals would be inhuman: sobriety is for people for whom the alternative is death, not a hangover. Anyway, it’s been tried, and it failed in the 1920’s and it’s been failing since the 1980’s. For recreational drugs, I like the Dutch solution: use is okay, supply and manufacture isn’t. This stops the police and courts wasting time convicting users, when they should be after the manufacturers and distributers.

Mood-altering recreational drugs are one thing, but what opiates and cocaine do is another. What The Economist gets utterly wrong is that the important issue is not how we treat existing addicts (though that’s an issue), but how we prevent anyone else becoming addicted.

Manufacture and distribution of hard drugs (opiate- and cocaine- based) needs to be treated as an assault on the safety and dignity of the People, if I may use a hi-falutin’ term. It's chemical warfare conducted by terrorists. Following Lester Freamon’s Rule ("You follow drugs, you get drug addicts and drug dealers. But you start to follow the money, and you don't know where the fuck it's gonna take you”) we leave the addicts alone, and deal with the suppliers, importers and manufacturers. Governments, or at least their police and intelligence services, know who these people are, and who are their lawyers, accountants, bankers, doctors and other civilian-side support personnel.

These organisations need to be disabled from the top down, and from the outside in. Without their lawyers, accountants, bankers, corrupt judges, policemen, customs and immigration officers, the business has difficulty operating, and while the men at the top can always recruit mules and dealers, the mules and dealers can’t recruit the men at the top to do the organisation. Remove one cartel, and the others will expand, which means it will be a sustained campaign, and not a pretty one. This is why it needs to be seen, not as a “war on drugs”, but as defence of the realm. A war on drugs wants to stop people getting high, which has been proven not to work. Defending the borders of the realm, and the health and lives of many of its citizens, from non-State terrorists who have financial resources that dwarf those of all but the largest multi-nationals and States, is an altogether less questionable aim.

This must be done with public and legitimate use of the State’s armed forces and intelligence services, and that requires the jurists to develop the doctrines needed to legitimise the use of military force against non-State criminal organisations based in other States. The voters, soldiers and politicians need to understand that preventing the manufacture and distribution of opiate- and cocaine- based drugs (or artificial syntheses of these) that threaten the lives, health and well-being and morale of those who take them is the exact same aim as preventing pharmaceutical companies distributing and promoting drugs with vicious side-effects. The aim is prosecuted in a more vigorous manner different manner because drug carteliers don’t stop when they are asked, fined or imprisoned. Drug barons only stop when they are in a grave. Pharmaceutical company CEO’s give up a little sooner than that.