The paper in question purports to describe odds of the author finding his ‘perfect partner’ as 1 in 285,000. To haul the paper marginally out of author Peter Backus’ navel he derives this figure with a personal variation on the Drake Equation, which describes the possibility of our galaxy harbouring communicating civilisations [click the link to see a nice interactive explanation of how the Drake Equation works].

The God of Whizz is as much a fan of whimsical investigations as the next educational deity, and very much a fan of how simple maths problems can shine light on apparently intractable problems.

But Backus’ paper is good only as a promotional piece with an apparently depressing result. Even so, it has generated a lot of publicity, thanks to the idea that Backus has hit upon some kind of magical equation for love (or the lack thereof).

The Drake Equation is a neat exercise in the effects of multiplying odds when you’re combining known and unknown values and an oft-heard criticism is that multiplying possibilities multiplies the possibility for error.

Backus’ equation substitutes Drake’s little-known vastnesses of space and time for the guesswork values of physical and emotional attachment. The error bar alongside his final number must be so wide as to make it usable only as an exercise in basic maths.

We can see a response to Backus’ huge odds against love in the anthropic principle. It is often said that the universe is fantastically unlikely ever to have taken shape, let alone to have allowed the development of intelligent life. And yet, we’re here.

The anthropic principle inverts this. It says, simply*, that the fact we’re here means it’s possible. The same argument meets Backus’ paper with the simple observation: “even ugly, picky people in small towns fall in love”, which becomes what I call the Amatory Principle (something I’ve just made up).

The Amatory Principle notes that people find love, all the time, everywhere, and in the unlikeliest of circumstances. It’s a staple of fiction, but it’s also true. Happiness in love is out there, ergo happiness in love is possible and whatever statistical rules say otherwise must be adjusted.

The punchline to all this is that Backus has a girlfriend! This is just fine, of course, because Backus has proved the Amatory Principle.

The grump in me says that I couldn’t give a fig if the whole exercise was for fun, because it has been laundered through various media as something of value, touching on the ineffable figures that underpin our lives, even if just with a nod and a wink.

I feel for the University of Warwick press officer charged with raising their employer’s profile as a seat of learning with a four-page bit of fun put out by a post-graduate. I would exhort him or her to watch the fascinating new BBC documentary series with Jim Al-Khalili looking at chaos, fractals and the equations that really DO say something about life on earth (if not the chances of dating a nice London girl).

* Because I’m not clever enough to say what the complex version of the Anthropic Principle (Weak or Strong versions**) is.

** Google them if you really want to know

It is often better to fail something in order to learn it better.

Here’s how the SciAm summarises the findings from recent research in the Journal of Journal of Experimental Psychology: Learning, Memory and Cognition:

In a series of experiments, [the researchers] showed that if students make an unsuccessful attempt to retrieve information before receiving an answer, they remember the information better than in a control condition in which they simply study the information. Trying and failing to retrieve the answer is actually helpful to learning. It’s an idea that has obvious applications for education, but could be useful for anyone who is trying to learn new material of any kind.

Quite. Drivers who don’t pass their test first time are apt to say (for their pride, if nothing else) that failure makes them a better driver. And this is something we at Whizz consistently tell students, parents and teachers: Don’t be afraid to fail.

Failure in Maths-Whizz is often constructive – it tells the tutoring engine that a student’s understanding of a subject may be incomplete, it allows the student to revisit the subject to reinforce her understanding and, given these recent findings, it may fix the solution – when the student finds it – more firmly in her mind.

This work has implications beyond the classroom. By challenging ourselves to retrieve or generate answers we can improve our recall.

This method is directly applied in a number of maths-whizz pencil and paper style exercises – where the student is asked to estimate the answer before proceeding with the detailed solution. But it also applies to those instances where a student at first fails a few questions, or an entire exercise.

The research is a reminder that whilst it seem unfair to expect students to provide answers beyond their comfort zone, this ‘pretesting’ effect could in fact better prepare them to hold onto that knowledge when later it is properly acquired.

So, if you’re a Maths-Whizzer stumped on a question don’t worry, just give it a try. If you fail first time, you might just remember it better! And if that isn’t encouragement enough, take it from Michael Jordan:

It has come to the attention of the God of Whizz that ‘maths’ or ‘math’ is a word too often used in anger than in scientific or mathematical description. It has become an epithet, almost.

Invariably, if a blogger, or news opinion writer, disagrees with a particular policy statement or bill the reader will be encouraged to ‘do the math’ or, less frequently, ‘do the maths’. By ‘doing the math’ the reader will – inevitably, it is assumed – see the folly of whatever policy/bill/etc. the writer is critiquing.

‘Doing the math’ is an especially popular pastime for critics of tax or government expenditure policies. Whether you find yourself agreeing or disagreeing with those policies is besides the point, because – as the God of Whizz righteously declaims – ‘math’/'maths’ is brought down by all this.

Why is this? Mathematics is a beautiful, abstract, science. As we’ve often pointed out, without maths, many of the fundamental scientific, economic and engineering principles on which we daily rely would be either still hidden to us, or at least staggeringly opaque.

But this does not make maths an objective arbiter of truth. Maths is a means, not an end, and many mathematical tools are only as good as their sensible application. If I use a perfectly good statistical method that nevertheless obscures the actual distribution of my data, then I have no more found the ‘truth’ using maths than if I had drawn a pretty picture that I felt best described my emotions doing my research.

Without batting on too much about this, it is fair to say that ‘doing the math’ is often only as rigorous or objective as the person doing it. If, by doing the maths, you purposefully exclude key information, or you make certain bad assumptions, you have misused the maths to make a personal/political/social point that fits your agenda.

You would be better off being honest about your moral or emotional impetus, or hedging your remarks. The problem with this is that simple thinkers like bold statements – cautious, careful commentators who understand the need for balance are often ignored, or derided. The God of Whizz bets one of his (many) arms that mathematicians are not in the habit of being as bold in their claims as those who purport to understand and apply the maths from a political or social standpoint.

And that – says the God of Whizz – is not good! The God of Whizz instead exhorts us all simply to respect good methods, clear thinking, and keep an open mind when the boundaries between maths and opinion seem to blur.

As an aside, he encourages us all to sign up our children to Maths-Whizz, so they are less likely to make the same mistakes that we do…

It’s easy to forget that the handful of men who visited the moon were sent there by tens of thousands of the best and brightest engineers, scientists, and – of course – mathematicians. One such was Don Eyles, a young maths graduate who ended up programming the software for the computer in the lunar module (BBC Video).

Just shows what you can achieve with a bit of maths. In fact, without a grounding in maths, the astronomers, engineers and scientists who worked on Apollo would have been as incapable of planning the moon missions as if they had been illiterate.

Check out kottke.org’s huge collection of Apollo 11 anniversary links – a feast of information and reminiscences.

If you’ve not yet done so (and what on earth are you waiting for? – excuse the pun) sign up for some online maths tutoring to give your child the best chance to take part in the groundbreaking achievements of the next forty years.

The human brain that lets us add, subtract, read, write, walk and chew gum (sometimes at the same time!) evolved from a brain that had different demands imposed upon it, most of which revolved around staying alive long enough to have offspring. So how have we co-opted brain regions specialised for navigating ancient woodland and savannah into helping us file our tax returns?

As reported in the National Geographic this month, one way is this:

Structures in the human brain once devoted only to visualizing spaces are now also involved in performing simple mental math…

According to the research, it seems the eyes do have it when it comes to reading our inner mathematical thoughts. Researchers have tracked eye-movements and identified the region of the brain that lit up when participants looked left, and the region associated with gazing rightwards.

They then used activity in these brain regions to show that participants tend to process numbers of different sizes as locations in space, an effect snappily titled ’spatialnumerical association of response codes’, or SNARC. The researchers predict that adders (not those adders) will mentally move their eyes rightward, whilst subtracters move them leftward.

If the predictions hold true, this would reinforce the idea that we think of numbers in spatial ways and that the wonderful flexibility of the brain enables us to handle abstract problems of number and language using older, more concrete mental skills (like figuring out where you are).

Of course, we are often taught maths using spatial concepts – number lines, manipulatives and so forth – and researchers acknowledge that this could be an artefact of the way arithmetic is taught to younger children, as hops along a number line. Adding (or counting on) is a rightward hop, and subtraction (or counting back) a leftward hop. Your eyes might naturally tend in one direction or another, depending on the operation.

Still, the fact that we teach with numbers on lines, or as floors in a building etc, might just be reflections of that innate tendency to ’see’ numbers in space. It would be interesting to test the authors’ predictions with novice mathematicians and expert ones. If memory serves, university mathematicians start to process numbers as they do language, just as expert musicians make a similar transition. Because simple 2D visualisations aren’t sufficient for thinking about Mandelbrot sets, or Riemannian Geometry the experts may show less of the whole eye-moving effect when thinking about maths.

The bottom line, as it always is, is that Maths-Whizz knows all this. We teach early adding and subtracting with leftward and rightward jumps, and lead students into abstract pencil and paper arithmetic at year 3 by encouraging them to visualise those jumps in blocks according to the numbers’ place value. e.g. 125 + 43 starts at 125, and then jumps 40 to the right, and another smaller jump of 3 more.

Which top ten? Football, Table-Tennis, obesity? No, no, and thrice no – TIMSS!

TIMSS is the catchily-titled ‘Trends in International Maths and Science Study’. The study is a quadrennial analysis of maths and science skills in primary and secondary-age children (two groups – 10 and 14yrs).

TIMSS placed English students 7th and 5th for 10 and 14 year-olds, respectively, in science, and 7th in maths at both age groups. More than 60 nations participated in the survey. This puts English kids, according to the BBC news site, ahead of many of our European competitors.

This improvement seems to have been at the expense of student enjoyment of the subject, as Schools minister Jim Knight noted. Whether this is because students are being tested more, or because they are actually being pushed to do well (and no child likes to be forced to study) is not within our means to say, but the results are surely encouraging in themselves.

The results also compare well with those for the 2007 Pisa survey of maths and reading, which rated the UK’s 15-year-olds ‘average’ in maths and reading, from a larger group of nations.

Less encouraging, sadly, are the TIMSS results for Scottish children. Scotland’s highest placing was 13th out of 49. There is clearly work to be done north of the border, and we’d hope our superb maths tutoring service might help scottish kids everywhere.

(Maths-Whizz is still appropriate for sassenachs, we might add).

DARPA, US military’s boffin-central, has put out a call for solutions to some of the most intractable scientific issues of our day. DARPA (which, incidentially, founded the military forerunner of the Internet, ARPANET) hopes this challenge will have the effect of:

“dramatically revolutionizing mathematics and thereby strengthening DoD’s [Department of Defense's] scientific and technological capabilities.”

Down the years one of the fastest ways to get a scientific breakthrough into the real world has been to get it into the military. From Galileo’s improvement and popularisation of the telescope as a military tool, to modern mathematics’ use in cryptography, DARPA presumably figures these hoped-for mathematical breakthroughs will benefit them (If anyone can find a military-industrial use for ‘optimising occam’s razor’ it must be them…).

I, for one, would be keen to know the fudamental laws of biology, though I suspect the maths may be be beyond me; besides, I really don’t have the time. So if you fancy a bash at some of the hardest problems known to the human brain, scroll down, though on your head be it if you militarise ‘information theory for virus evolution’. Answers on a postcard, as usual.

(NOTE: Please submit only ONE ground-breaking mathematical discovery of international importance per postcard.)

• The Mathematics of the Brain: Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.
• The Dynamics of Networks: Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the social sciences.
• Capture and Harness Stochasticity in Nature: Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.
• 21st Century Fluids: Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.
• Biological Quantum Field Theory: Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?
• Computational Duality: Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
• Occam’s Razor in Many Dimensions: As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.
• Beyond Convex Optimization: Can linear algebra be replaced by algebraic geometry in a systematic way?
• What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?: Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate novel materials?
• Algorithmic Origami and Biology: Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.
• Optimal Nanostructures: Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembly.
• The Mathematics of Quantum Computing, Algorithms, and Entanglement: In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.
• Creating a Game Theory that Scales: What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to differential games?
• An Information Theory for Virus Evolution: Can Shannon’s theory shed light on this fundamental area of biology?
• The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?
• What are the Symmetries and Action Principles for Biology?: Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and variability.
• Geometric Langlands and Quantum Physics: How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?
• Arithmetic Langlands, Topology, and Geometry: What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?
• Settle the Riemann Hypothesis: The Holy Grail of number theory.
• Computation at Scale: How can we develop asymptotics for a world with massively many degrees of freedom?
• Settle the Hodge Conjecture: This conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.
• Settle the Smooth Poincare Conjecture in Dimension 4: What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?
• What are the Fundamental Laws of Biology?: This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.

…hit a very small ball into an even smaller hole, with weapons singularly ill-designed for the purpose.

recently made public to the USA’s Congress his enthusiasm for maths and science.

Whilst golfers hardly reflect the kind of demographic that needs most to benefit from good math and science education, it is nevertheless no bad thing that Mr Mickelson should make such a public plea. Sportsmen and women are too rarely associated with educational initiatives, and this is especially so in the UK.

Mickelson’s Teachers Academy, setup in 2005, trains selected teachers in new ways to convey the excitement of science and math in creative ways. His testimony to Congress included the oft-heard but too-little acted on warning that americans risk falling behind the rest of the world if they fail to train the next generation in the sciences and math.

This concern of losing out in the global race for ideas and skills features high in the minds of educational experts in the UK, but somehow the obsession with ‘knowing one’s place’ damns some people unfairly when they make public statements about areas seemingly beyond their remit.

In the UK we should applaud anyone who speaks out in favour of knowledge and learning, whether it’s Wayne Rooney or Stephen Hawking. And we don’t even need Mr Rooney to say earnestly how he relies on the advancements of science in his everyday life or understands the pleasure of calculating the perfect bicycle kick with trigonometry – we just need him to say that knowledge is its own good, and that sciences and math are the keys to the world.

It’s not much to ask.