Category Archives: Statistics

Of Cats and Cashflow: Human sentimentality and the flaw in economic rationalism

Last Christmas, I paid $5000 for a cat.

$5000.

For a cat.

“Cat” here, in case you should be wondering, is not the title of an avant garde piece of sculpture by some breaking new artist, or a colloquial reference to a rare wine or other exclusive gift for a loved one. Nor indeed, anything special in the feline department.

Just an ordinary cat that my 9 year old daughter had saved her pocket money to rescue from the Animal Shelter. Yes, okay, it’s accepted family lore that he is actually a pedigree animal who somehow found himself down on his luck on kitty skid row – but I can accept there may be a degree of parental self-delusion in that particular idea.

Whatever his back story though, as the warm summer evenings of 2013 began to lengthen, heralding the winding down of business and arrival of the holiday season, all thoughts of casual beachside barbecues and Christmas relaxation were rudely dashed for me one Saturday morning as young Pedro – having manfully picked a fight with a passing car – dragged his sorry frame into the house and collapsed theatrically in the middle of the living room floor.

After a quick cat scan at the local veterinary hospital (no, not a moment of levity playing on my feline friend’s biological order there – a real actual honest-to-goodness “cash up front please sir” CAT scan cat scan) showed up the incontrovertible evidence of a clean and comprehensive break right through the young street fighter’s pelvis, the therapeutic choices came to a quick fork in the road. One path led to major surgery, emptying of savings accounts (“kids – hands up who’s going to University. Not so fast there you two”), and having a half-shaved grumpy convalescing cat locked in a cage in our cosy house through the warmest weeks of summer. The other, to a quiet, calm, fully funded holiday season. Even a couple of weeks of really nice vacation. As well as the sticky point of explaining to my daughter why her precious kitty wouldn’t be joining us for Christmas dinner.

The path we chose (and I say “we” here entirely in the blame-shifting and shared responsibility sense – my wife’s version of this story may differ on the precise extent to which each of us couldn’t stomach the tough decision making) probably tells you everything you need to know about why I’m never likely to make the annual list of Australia’s 10 hardest hearts. And why you shouldn’t take my advice on anything to do with finance.

The point is, this doesn’t qualify as an investment decision. It’s not like I had some brilliant plan to parlay this $5000 outlay into a major stream of retirement income. Even if the cat in question is possessed of the kind of dashing good looks that could make him a major star in pet food commercials…if he could at some point stop trying to take a chunk out of any hand with the temerity to pat him without explicit permission.

No, it just turns out that little tiny titanium screws are really expensive. If you want them put somewhere useful by a veterinary surgeon, anyway.

The much pampered and perhaps overly tolerated Pedro - a few lives down from his initial quota of 9 perhaps, but still going strong as an extended metaphor for social relativism. And definitely not just a shameless attempt to elevate my viewing stats through use of a cute cat picture.

The much pampered and perhaps overly tolerated Pedro – a few lives down from his initial quota of 9, but still going strong as an extended metaphor for social relativism. And definitely not just a shameless attempt to elevate my viewing stats through use of a cute cat picture.

And there, laid bare for the world to see, lies the fundamental flaw with economic rationalism. People are not reliably rational actors on the world stage – we all bring our personal values, idiosyncrasies and biases to economic decision making.

For those of you who might not be fully familiar with the concept, economic rationalism (market liberalism, for readers from outside Australia) is the dogmatic view that markets and money can always do everything better than governments, bureaucracies and the law.

In the more prosaic words of Michael Pusey – Professor of Sociology at the University of New South Wales: “Forget about history and forget about national identity, culture and ‘society’…Don’t even think about public policy, national goals or nation-building. It’s all futile. Just get out of the way and let prices and market forces deliver their own economically rational solution.”

This philosophy underpinned a sharp step to the right across much of the Western political sphere in the 1980s and 90s – think the Hawke-Keating-Howard years in Australia, Thatcherism and its correlatives in Europe – and has more recently been used as the basis for a strict balance sheet approach to management in many areas of wider society – education, housing, the arts, even environmental policy.

This deference to accounting undeniably has a certain elegance to it – a simple coherent narrative that can easily be painted on a placard, or broadcast in a 6 second sound bite. Like Creationism re-packaged for a political audience though (and with many of the same elements of true belief and ideological fervor), the sneaky trick here is that while this is dressed up as analytical economics, really it is all about political philosophy – the ideology of unfettered personal freedom. Don’t get me wrong – it is entirely proper for economic rationalists (or anybody else) to allow value judgments about freedom to define their policy prescriptions. It is improper and, more importantly, incorrect, however, to claim that these ideas flow simply from the laws of economics, and possess some sort of inescapable mathematical truth.

The beauty of mathematics, of course – the reason political and social movements have long sought to co-opt it to their crusades – is that it gives defined, absolute solutions. Put your numbers into an equation, and you get an answer at the end. To as many significant figures as you like. This allows us to do amazing things – like build giant flying machines from aluminium and carbon fibre that can carry hundreds of passengers around the world in a matter of hours. Or land a spacecraft on the surface of Comet 67P/Churyumov-Gerasimenko hurtling through space 510 million kilometres from Earth.

Real world problems though – especially anything touched by the inordinate complexity of human social psychology – commonly fail to lend themselves to mathematical solution. The real world simply has too many possibilities and undefined variables – such that equations have no solid foundations they can be anchored to.

To make problems tractable – to allow mathematics to give us that pure, crystalline answer – we usually make certain assumptions to tie down the open ended possibilities and give us a solvable domain to work within. The danger here though is of ending up with what the great 20th Century physicist and public champion of science Richard Feynman used to call a spherical cow argument (readers of my earlier posting on University fees “More Pennies for Your Thoughts” will have seen a longer explanation of this concept) – an assumption that, while making your equation solvable, also removes any meaningful relationship to the physical system it purports to represent – and when that happens the clean precision of a mathematical solution can be misleading. Or worse.

The NASA engineers plotting the journey of the Mars Climate Orbiter to the Red Planet in 1999 produced incredibly precise solutions. They also assumed the output of one of the key pieces of navigation software on the Orbiter was in metric Newtons of force…when it was actually in pounds of thrust. Oops. This rendered their solutions elegant, precise…and dead wrong, with the $USD 125 million satellite coming in too close to the planet and breaking up in the Martian atmosphere.

Perhaps more than such elementary cases of error, however, the important thing to grasp in a social context is that you can use framing assumptions to distort the result in any direction you might desire. Want to argue against the opening of a new coal mine? Include some cost assumptions about externalities like atmospheric pollution, environmental risk, and increased traffic to show the economics don’t stack up. Or as I showed in an earlier blog, want to argue in favour of higher University fees? Make some helpful assumptions about the financial advantage accruing to a graduate while discounting the societal benefits and increased tax revenue from a more educated population.

Even in the best of circumstances though – if we assume (at the risk of vanishing into the never ending hall of mirrors that is self-referential logic) all our assumptions are correct and appropriate – the critical point to remember is that economics cannot tell you what is the right choice. Morality and values do not drop out of financial equations like wisdom paying out from a philosophical poker machine. Any investment decision comes down to a balance of short term sacrifice against long term gain. Instead of spending your money on something now, you invest it in the expectation of gaining greater reward at some future point.

When it comes to quantifying outcomes – basic economics – that can be a pretty straightforward calculation. “If I have $1000 now, would it be better to stuff it in my mattress or invest it in government bonds for 10 years”. Okay, there are still some assumptions to make about yields and the potential of unexpected events like your significant other throwing your mattress in a skip while you’re at work. Or a plunge in the commodity price on which a government had based all its economic projections, driving it to default on its debts (Hmmmmm…so how is the iron ore market going, by the way?)

By and large though, you can produce a pretty robust solution to that kind of question and say which one is likely to give you the higher return over a 10 year period.

Defining what the sensible decision is based on those results though – now there’s the challenge – with a crack arising in the logic around defining how great a long-term premium is required to make the short term sacrifice worthwhile.

Let’s say that Mike believes that the pleasure he derives from eating a custard slice is an appropriate trade for the 30 seconds it might shave off his life (or the hour in the gym it will take to work off all that delicious vanilla flavoured excess), whereas Susan doesn’t think the momentary pleasure of the creamy mouthful is worth the sacrifice. Who is right? Both are, of course. It’s a question of values and opinion, it has no absolute solution – no single true answer that trumps or invalidates all others.

Orthodox economics is very clear that policy recommendations must rest on both economic analysis AND a set of values. There is no objective adamantine economic ‘truth’ – the social implications of financial modeling depend on your personal beliefs and values.

Even Milton Friedman – often held up as the philosophical father of Economic Rationalism – understood this qualification, stating:

“As Liberals, we take freedom of the individual, or perhaps the family, as our ultimate goal in judging social arrangements.”

No special pleadings or claims of incontrovertible quantitative support there – Friedman is perfectly comfortable acknowledging that his social policy ideas (a fountainhead that fed both Reagan and Thatcher in their glory days of social engineering and reform, let us remember) are based on an ideology. And that’s fine. On that basis, you can assess and debate his arguments, and decide for yourself whether that’s the model you would like to see underpinning the society you live in. Friedman, unlike the hardline Economic Rationalists who have followed in his intellectual wake, allows that alternative social models may be equally valid if you don’t happen to share his values.

Like, for example, valuing a deeply ungrateful cat (and the happiness of a small child) more than a new sofa or a week in Paris.

And hey – at the end of the day, even if we were all perfectly rational actors making our life decisions on the basis of pure logic and mathematics, that might not actually be the lasting social panacea the Economic Rationalists hope for. You’ve seen what happens to the planet Vulcan in J. J. Abrams’ 2009 Star Trek re-boot, right?

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Fairy Tales on Shaky Ground – Scientific understanding and the Italian court system

On the 6th of April, 2009, a 6.3 magnitude earthquake centered 9.46 km beneath the Abruzzo region in central Italy devastated the city of L’Aquila, ripping the historic heart out of the city and killing 309 people. While the physical scars from this tragedy are fading, cultural aftershocks are still rippling through the scientific community, and reached a peak unexpected by many this week with the conviction of six Italian scientists and a former government official for involuntary manslaughter.

The seven – members of the Italian National Commission for the Forecast and Prevention of Major Risks at the time of the earthquake – were sentenced to 6 years in prison, and ordered to pay court costs and damages amounting to some 7.8 million Euros.

Their conviction was based principally on a number of statements made six days before the damaging tremor, downplaying the likelihood of a major earthquake. Given the manifest impossibility of reliably predicting Earthquake occurrence with our present understanding of seismic processes, the legal precedent for this is presumably drawn from the Brothers Grimm, with imprisonment the prescribed punishment for failing to spin straw into gold.

Earthquakes are caused by the release of energy as fractures propagate through rocks. They are focused in particular regions where creeping deformation deeper in Earth leads to the build up of stress in the more brittle rocks near the surface. Once a fracture has occurred, the crack remains a discontinuity – a weakness – and tends be a site of further failures in the future.

If you live near such an existing fracture – or fault – the likelihood of experiencing an earthquake increases dramatically. This much we can say with confidence. Certainly, in the long view, no-one can claim to be surprised by the damage wrought on L’Aquila, given the city is built on an ancient lake bed known to provide a geological framework that amplifies the local effects of seismic waves, and has been devastated by earthquakes on no fewer than seven historical occasions, in 1315, 1349, 1452, 1501, 1646, 1703, and 1706.

But when will the next Earthquake happen? Now this – the 7.8 million Euro question – is the holy grail of seismic hazard research, and to date, there is no answer. Anybody who tells you differently is probably emailing from Nigeria to offer you ‘the investment opportunity of a lifetime’.

Despite all the work by teams of dedicated and sometimes brilliant researchers over the past century or so, all the collection of data and analyzing of patterns – even for the San Andreas Fault in California, probably the most intensely monitored fault zone in the world – no distinctive and reliable precursor patterns for major earthquakes have ever been recognised.

To hold someone responsible for failing to predict an earthquake on the basis of preceding activity makes all the statistical sense of having your first tip on Melbourne Cup day romp home, doubling down your house on the trifecta in the next race, and then suing your bookie when the horses fail to place.

So how can this miscarriage of justice have occurred? Why weren’t the charges thrown out at the earliest opportunity?

Fundamentally, as I wrote last week (Three Monkeys, Ten Minutes – Scientists and the Importance of Communication Skills – WordPress 18/10/2012):

“Society is complex, and people hold views for all manner of reasons – personal, cultural, logical, or religious, among others. We [as scientists] do not have to share those views, but we do need to appreciate and respect their reality”

When I wrote those words, I hadn’t expected to be confronted by such a glaring (and dark) example of this relationship at work quite so quickly. Scientifically, the question of earthquake prediction doesn’t even get off the ground, but to a broader population un-tutored in statistics and the language of scientific uncertainty, a population here stung by a great tragedy and searching for someone to blame – a sadly common human trait – the Committee’s statements painted them with a target.

People are incredibly good at recognising patterns. This, as much as anything, is the key to our astonishing success as a species. Unfortunately, the flip side to this is that we look for – and expect to see – patterns even when they are not there. This makes us very bad at evaluating the true risk of rare events.

James ‘the Amazing’ Randi is conducting a long term demonstration of this phenomenon. Every morning he writes on a card “I, James Randi, will die today”, which he then dates, signs, and keeps in his pocket in the knowledge that it will one day (may it be far in the future) be a fitting final demonstration of how apparent correlation can be manipulated to lead our minds astray.

Richard Feynmann related a similar story in his memoir “Surely you’re joking, Mr Feynmann” – where he writes of hearing the phone ring in his University dormitory and having a sudden premonition that his grandmother had died. She hadn’t. The phone wasn’t even for Feynmann, and his grandmother continued in rude good health for some time to come. The point is, we have such thoughts and intuitions all the time – for the most part, they don’t turn out to be correct, but occasionally the fates line up. When they do, the glorious pattern-seeking engines that are our brains get a kick of reinforcing dopamine to say ‘job well done’ and we forget about the 999 previous times it hasn’t worked and start to see a correlation.

If you live near a fault line, you will, inevitably, experience earthquakes. Sometimes big ones, often small ones. Sometimes a large one will be preceded by small ones. But usually not. The stochastic patterns – one earthquake here, two the next week, none for six months – have no significance.

There is a real tragedy at L’Aquila, and there are people who should be held to account. But they are not the scientists who gave an accurate representation of the processes at work beneath the town, and the statistical meaninglessness of looking for patterns in the tea leaves of local seismic activity. Rather, the guilty parties – those who should have known better – are the officials and engineers who built structures – schools, gymnasiums, dormitories – in the city that were not designed or constructed to withstand the well known and historically proven earthquake risk.

So, we find ourselves at the end of act 1 in our re-imagining of Rumplestiltskin – the Miller’s daughter has proven unable to spin her straw into gold and the King is about to imprison her in the highest room of the tallest tower. Perhaps in act 2, Uri Geller will step up to the title role and offer to solve her problems by magic in exchange for first authorship on the resulting scientific paper.

I wouldn’t start from here Gina: Historical contingency and the anthropic principle

In science we seek to explain and predict natural phenomena, and part of this process is the identification or construction of cyphers – representative examples or ideas through which we can encapsulate and illustrate our arguments. These fill a significant role in making otherwise irreducibly complex systems tractable, helping us get our heads around – and explain to others – multi-dimensional and abstract concepts. At the risk of getting a bit too George Lucas early in the essay though, in this rhetorical power there is also a dark side – apply a cypher the wrong way and it changes from being an illustrative device to a philosophical delusion that can make ridiculous conclusions seem reasonable, so we sometimes need to take a step back and check the fundamental concepts underlying our thinking.

Alongside her vigorous public advocacy for government deregulation and the lowering of taxes for the wealthy, Gina Rinehart (richest person in Australia and an excellent candidate for poster-child should the Federal government decide to move on from giving the tobacco industry a thorough and long overdue kicking and run a ‘money can’t buy you happiness’ campaign as a contribution to the nation’s health) showed her magnanimous side in August of 2012 by offering some free advice to the less fortunate working citizens of Australia struggling to make ends meet in the face of spiraling living costs:

“If you’re jealous of those with more money, don’t just sit there and complain. Do something to make more money yourself – spend less time drinking or smoking and socialising, and more time working.”

Now, whatever you take from that personally (and I’ve got to think there aren’t many people having that particular mantra tattooed across their chests in gothic script as a life changing rule to live by) the interesting thing to realize is that Rinehart’s suggestion probably made absolute sense to her. I say only ‘probably’ as it’s not impossible she’s perfectly aware how offensive her comments were to a large number of people and was just doing it to wind up Wayne Swan, the current Federal Treasurer. In fact, perhaps she and fellow mining tsar Clive Palmer have agreed a billionaire’s wager, much like brothers Randolph and Mortimer Duke in the 1983 movie ‘Trading Places’ and are taking it in turns in a colossal game of ‘top that’ to see who can make Swan rupture an aneurysm first. It would certainly explain a significant number of recent media statements. But I digress – Rinehart’s modern take on ‘let them eat cake’ probably made absolute sense to her because of the perspective she brings to the issue. Mrs Rinehart has, after all, worked hard and made many sacrifices to reach the stratospheric levels of wealth that she today enjoys, and presumably sees that path as the wellspring of her success. The same might not have been achieved, however – the same journey indeed, might have not even been possible – without the support, inspiration, and mentoring (not to mention mining leases) of her visionary and highly successful father, the prospector and – ultimately – iron ore magnate, Lang Hancock.

Rinehart might want to tell herself “I could have done it all on my own without the privilege and wealth I was born into” – and who knows, that might even be right. But the fact of the matter is that, outside of a whacky Disney movie (picture it – the ghost of Steve Jobs (played by Ashton Kutcher, obviously) visits Bill Gates (Kermit the Frog playing against type to prove his great comeback playing opposite Jason Segel in last year’s Muppet franchise reboot wasn’t just a lucky break) and offers to create an iGod app to cure all childhood disease in the third world if Bill is prepared to go back in time to live his life again as the son of a struggling but decent single mother (Sandra Bullock). To win the bet Bill has to prove that he can still drop out of college and found the world’s most successful software company without the benefits of an elite private school education and the support and connections of a close-knit and loving family with a lineage of bank directors and successful lawyers stretching pretty much as far back as the Mayflower. I’d pay to see that), that reset will not – can not – happen. Rinehart will never see whether success is possible without the benefits of her upbringing and circumstances, any more than Rick Blaine will ever know if Ilsa and he might actually have lived happily ever after if she’d turned back at the boarding gate and ditched Victor Laszlo and the Czech resistance to stay with him at the end of Cassablanca.

That’s the way historical contingency works. It’s not relevant to ask the question ‘how likely is that’, or ‘what else could have happened’, because as soon as something does happen, infinite possibility collapses down to a single reality.

How likely is it that you could pick the Lotto numbers for Tuesday’s draw? It’s a trivial calculation – a 6 in 40 chance that one of your numbers is first out of the barrel, then a 5 in 39 chance of the second number as well, and so on – for an overall probability of about 1 in 26 million. Too easy? Okay – how about something more challenging – what’s the likelihood of picking the lotto numbers every week for the next year? One in about the order of 10381. That’s a number so vanishingly small as to have no meaningful way to even conceptualise it – about as close to a definition of ‘statistically impossible’ as you could hope for. To put it into some sort of context, there are calculated to be only about 1080 atoms in the visible universe. And yet – if you look back at the historical record, there it is – 6 numbers have come up every week, and you can see that record there in black and white – for a year and more – as far back as you’d like to the first live drawing in Australia back in 1972. The impossible has become the certain. And that’s the point – it’s irrelevant to ask the question “how likely is it that this particular sequence could have happened?” – because the simple fact of record is that it did. Probability has no relevance to history.

Now, by another seemingly astonishing coincidence (yes, it’s a narrative leap of epic proportions, but stick with me on this one), all aspects of the structure of the Universe and the laws of physics by which it operates are within a narrow range of values consistent with the existence and operation of life as we know it. The Universe is old enough to have created enough ‘heavy’ elements (everything other than the hydrogen and helium created in the Big Bang) through solar processes for we carbon-based life forms to exist on a nice rocky planet – but not so old that stars like our Sun have turned into dim white dwarfs incapable of bathing us in sustaining warmth. The cosmological constant is large enough to have stopped the Universe collapsing back in on itself, but not so large that rampant inflation stopped matter from coalescing to form stars…the list goes on.

Some people take this as a cornerstone of a theistic viewpoint (the universe could only be so perfectly attuned to the needs of life if it was designed by a creator). In a philosophical position known as the Strong Anthropic Principle, others – in what to me has always sounded rather uncomfortably close to a re-hash of the religious approach without the fancy clothes and awe-inspiring architecture – advocate, that the Universe is ‘compelled’ in some sense for conscious life to eventually emerge.

The obvious fallacy in these ideas though is that, like the ‘impossible’ prediction of an entire year’s lotto numbers, it implies that there is an alternative to the historical record. How likely is it that the universe we live in could be so perfectly suited to the evolution and function of biological life without some guiding hand and/or Universal compulsion directing it? The thing is, of course, that’s not even a valid philosophical construct – because the very fact you’re here to ask that question establishes pretty effectively that the Universe is, indeed, finely suited to your existence. To ask how it could have evolved differently is like the old joke about asking for directions in Ireland/the Countryside/Tasmania/insert-name-of-region-you-wish-to-denigrate-here – the punchline being “Well first of all, I wouldn’t start from here…”

What this drives us towards then is an acceptance of the less extreme Weak Anthropic Principle – which runs along the lines of ‘because intelligent life could only exist under the time and conditions we see around us in the Universe, it shouldn’t really surprise us that, as (nominally) intelligent life forms, those are the conditions we see’. It may be nothing more than a simple logical construction that doesn’t help us to explain or make useful predictions about anything else (and thus cannot be called a theory in any meaningful sense), but at least it has the advantage from my perspective that it doesn’t require us to start from an egocentric belief in the miraculous or predestination.

So thanks, Mrs Rinehart, for helping me to embrace my inner doubts and see that historical contingency means we don’t need to believe in our own specialness. The moral of the story I suppose, should one be desired, is that maybe instead of worrying about our position in the Universe and what it means, we should all be glad – and grateful – for what we’ve inherited.

More pennies for your thoughts? University fees and the Grattan report

“Graduates…have attractive jobs, above-average pay and status. They take interesting courses and enjoy student life. I think they are getting a bargain compared with their lifetime earnings potential.”

So says Andrew Norton, higher education programme director at the Grattan Institute, in his recent report ‘Graduate Winners: Assessing the public and private benefits of higher education’. Norton’s principle thesis is that graduates, rather than society as a whole, are the beneficiaries of higher education – and should therefore pay more, potentially much more, of the true costs involved in providing that education.

Discussion around the funding of higher education is important. Indeed, I would agree with Norton that a university education provides graduates (and even those students who do not graduate) with significant opportunities and benefits, so it is fair to question the degree to which an individual should contribute to the costs of that educational experience. But to follow the accounting approach laid out in the Grattan report is to cede an argument that should be philosophical and sociological to the realm of economics. It’s like the old logical fallacy “So have you stopped beating your wife yet?” By adopting the neat rhetorical device of comparative earnings, Norton and others like him are attempting to make the debate about quantifying the benefits graduates accrue, rather than what a University education is really for.

For all it’s careful analysis and sound-bite friendly calculations though (quotable statistics are a much easier sell than philosophical nuances, after all), when you look behind the numbers, Norton’s study is founded on what may be a less than secure foundation – the assumption that the higher lifetime earnings (and other benefits in relation to the general population) of graduates arise explicitly because of the degree they have obtained. But hang on a second, let’s unpack that assumption – because what Norton seems to be doing here is committing the schoolboy error of a equating correlation to causation.

How so? Well, are the higher earnings of graduates truly related to their University education, or are both simply related to another controlling variable? Since the 1950s, by way of analogy, both atmospheric CO2 and obesity levels in Australian society have increased sharply. To imply a causative relationship would be to suggest that in some way atmospheric CO2 causes obesity – as if we’re all just making our own carbohydrates directly through photosynthesis, perhaps – whereas in reality both are symptomatic of the common controlling variable of increased wealth.

In essence, the problem for Norton here – as he himself recognises in the inner workings of the report – is that the comparison between graduates and non-graduates is not unbiased. Yes, there are wonderful success stories of prodigiously driven, inspirational individuals who forgo the graduate path to achievement – stand up and take a bow Richard Branson and Steve Jobs – but in general, merit-based entry criteria mean that it is a brighter, more ambitious, and more self motivated cadre that undertake University education. If we also assume that career and business success correlates strongly to the same aspects of intelligence and drive, then it should not be a surprising observation that graduates are in the top bracket of career earners. How, then, do we calculate how much of the extra earning of graduates should be attributed to their University education, and how much to their innate ability?

Now here’s where I’m eternally grateful to Norton because, like a magician revealing how the illusion is performed, he tells us how it’s done. Admittedly in an appendix where an over-worked education reporter with a filing deadline to meet isn’t exactly likely to stumble across it. He assumes a number. Empirical basis? Scientific calculation? Theoretical underpinning? Nope. An arbitrary 10%. We’ll just assume University graduates enjoy a 10% earnings advantage due to their innate ability, and the rest of their career success is the result of their University experience.

Now, yes, this assumption is critical to make the calculations tractable so Norton can come up with his headline-grabbing $600,000 lifetime earnings differential…but the flip side is that the modeling is then simulating an artificial system rather than the behaviour it purports to capture. It’s like the old joke about a physicist charged with figuring out how to increase the milk production of a herd of cows, whose solution begins “First, assume a spherical cow…”

Norton does allow in the appendix for alternative calculations with an ability premium of up to 40%…but why stop there? Why not 50%? Or 100%? Or maybe they start with a premium of 150% but all that ‘student life’ they enjoy actually stunts their achievement. Okay I may be guilty of reductio ad absurdum here – but the point is that the ability premium has no innate basis – it exists only for that convenient mathematical purpose. There is no way we can resolve whether 10, or 20, or 200% is the appropriate figure to use. Like a Chinese high speed train project then – the Grattan analysis is built to look impressive and modern, but laid on potentially insecure foundations.

Why is that important? Surely the comprehensive modeling and calculations Norton undertakes are sufficiently robust that the conclusions of the report can’t be undermined by this one trivial simplification, can they? I’m not so confident on that score.

Let me illustrate by way of a detour through my own professional back yard. Physicist William Thomson (later Lord Kelvin) – a towering scientific intellect acknowledged as one of the greatest exponents of thermodynamics of the 19th Century – ‘proved’ in 1862 that the Earth was somewhere between 20 and 400 million years old. Earth scientists of the day thought that figure far too young to account for the global history evinced by the geological record, but none could fault his calculations. Indeed, Thomson’s calculations were accurate – brilliant even – and still stand as a valid construction. But they produce the wrong result. Out by a factor of at least 10, with the Earth’s actual age – should you be interested – now measured to around 4.54±0.05 billion years. How can this be? Because Thomson based his workings on the simplifying assumption that the Earth lacks an internal heat source, when in actuality radioactive decay has been continuously pumping out heat throughout geological history.

Although numbers may look good when quoted in a nice banner headline, any calculation, no matter how exquisitely conceived and accurately undertaken, is only useful if the underlying assumptions are true.

The relationship between higher education and society is a social compact that should be open for ongoing discussion, and as a part of that, we should be debating how Universities should be funded. In that context, the Grattan report should be seen as an important contribution, offering a coherent and well argued monetarist view of how the University system should operate. But it is nothing more than that. And if you think the economic modeling Norton presents should be privileged over other philosophical and sociological viewpoints in the discussion of the University system…I have a friend in Nigeria who would like to talk to you about a fortuitous windfall he’d like your help with.