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Speech: Brian Schmidt's mathematical argument
by:Brian Schmidt
From:The Australian
February 09, 201212:00AM
MATHEMATICS is a uniquely powerful toolbox of humanity. Unlike other things, mathematics is logically self-consistent and things are either right or wrong.
Once something is proven right, it is not in question. It is this certainty that makes mathematics such a valuable tool for us.
Everyone in Australia - and I mean everyone - needs to be mathematically literate, or numerate as we like to say, and our country needs many people to be more than numerate: we need people to be highly skilled.
For me, the tools of mathematics go hand in hand with the astronomy I undertake. Each day I spend more time using mathematics than any other activity. I took eight classes at university in mathematics, almost as many classes as I did in physics, and twice as many as I took in astronomy.
Now, you may be thinking that I am special - but let’s just look at my family. My father is a biologist, studying the populations of fish stocks in Alaska and now Canada - he uses sophisticated mathematics every day to understand exactly how to ensure that fish stocks remain at healthy levels into the future - as people fish, or dams release water, or glacial run-off slows or speeds up. Ah, but he is a scientist, you say. True.
My wife is an economist - whom I met at Harvard. Her education in economics has almost as much math in it as mine. Solving challenging coupled differential equations, undertaking sophisticated statistical tests - all to ensure that economies work efficiently at allowing their people to be prosperous - it is way more than simply bean counting.
But we all have PhDs. My Australian cousin and her husband who work in the mining industry as engineers - maths is the fundamental basis of their work, and, for that matter, Australia’s ability to extract minerals and become one of the world’s most wealthy countries.
My other cousin and his wife are farmers in Western Australia who do precision farming, where fertilisers and seeds are linked to a GPS system, and planted out at optimum values - all calculated by them using, you guessed it - math. Farming runs on tiny margins - a few percent – and this sophistication allows them to make money when others go bankrupt.
My brother-in-law in Sydney is a drainer - when he gets his trigonometry wrong, shit literally happens. His son is a commercial airline pilot - math is a matter of life and death for him, and of course, his passengers. I could go on and on. My family is much like any other one in Australia.
Most people who have skilled jobs in Australia have mathematics at the core of that skill base. But everyone needs math. In the modern world, math forms a fundamental basis of interaction with the world. Is my superannuation enough? Can I afford this home loan? Which telephone plan gives me the best value? Do the numbers the politicians quote on TV add up? To answers these questions - questions we all need answers for in order to be successful citizens - requires a competence in mathematics.
I made my first trip to Australia in 1980. If one looks at the GDP per capita of Singapore, compared to Australia, Australia was twice as rich. In 2010, despite the great economic conditions and strong Aussie dollar, Singapore was richer. And here is a country with no commodities other than its people, and useful location at the junction of the Indian and Pacific Oceans.
Over this period, Singapore has been among the top performers in educating its population as measured by the PISA tests. Australia has not performed poorly, but not as well as the best countries. The OECD says better educational outcomes are a strong predictor for future economic growth.
Imagine if Australia could combine our innate physical wealth with one of the world’s most educated workforces. The prospects for our country would face would be staggering. So if I cannot convince you with the economics - let me appeal to something else. New Zealand is one of the highest performing nations now at educating its population - significantly outperforming us. Do we really want to get walloped in this trans-Tasman competition? I would be happy with a draw at the top of the table.
So, how do we improve ourselves? Let’s look at the OECD’s findings here. It isn’t rocket science, although it could lead to some. The best school systems were the most equitable – in which students do well regardless of their socio-economic background. High performing school systems tend to prioritise teacher pay over smaller class sizes. High performing systems allow schools to design curricula and establish assessment policies but don’t necessarily allow competition for students.
So a fundamental mathematical education for all of our citizens, founded on the basics, is a crucial ingredient for our future prosperity. But we need not be afraid to move on with the times as well. When I was in Stockholm I got to meet the other Nobel Prize winners. We appeared on the BBC for an hour-long program called Nobel Minds.
When we were asked if there was anything we should be teaching our kids, remarkably, we all agreed on the same thing - this was three physicists, a chemist, two biologists, and three economists: we need to teach the idea behind uncertainty - and with it probability.
Facts and figures are usually filled with uncertainty and to understand what is going on requires us to come to terms with errors, uncertainties, and the notion of probability. I am reminded of this continually with the obsession that we have in Australia for running polls of the popularity of the Government and the opposition.
I have counted 33 Polls over the past 12 months - Nielsen and Newspoll - that have asked questions such as: Who do you prefer as the next prime minister? These polls typically survey just over a 1000 people, and they have what is described in the fine print as a sampling error of around three per cent. A week ago The Australian Newspoll reported the Prime Minister’s numbers have flatlined. Yesterday, we saw Nielsen report a six per cent jump.
This is great for newspapers. Every poll is news, because the sampling error makes every poll different. The two results I just reported, when looked at the rate the polls are done, are completely consistent. A three per cent change is reported to be statistically signficant in the newspapers - what does that mean? That means that 68.3 per cent of the time polls will give a number that falls within a +/- three per cent band. One in three polls will lie outside of this band, or 10 polls per year.
The six per cent change reported as highly statistically significant, I’ll translate for you. Only one in 20 times would such a deviation occur by random chance. But it was the biggest fluctuation of the year! And we had 33 polls. It is expected to have such a fluctuation by random chance.
The trends shown in the polls are valid, but for heaven’s sake – how about doing less frequent polls with more people surveyed - so we actually learn something, rather than having confected stories every two weeks about random fluctuations in samples? The media are feeding on the public’s ignorance of statistics in this instance. Maybe that is too strong - I do not even think the media knows what it is doing in this instance.
I also see the ignorance of statistics [and] uncertainty as one of the principal problems behind the climate change debate around the world. It is imperative to understand uncertainty to understand the climate change debate, but since the public doesn’t have these concepts, scientists skate around the issues, simplifying the truth to the point where it is no longer right.
While mathematics is perfect, it doesn’t always make it easy to predict the future, even with perfect knowledge. The Earth’s climate is what we call a giant non-linear system – often referred to as a chaotic system. Infinitesimal changes lead to significantly different outcomes. We can characterise general behaviour but it is hard to gauge its behaviour exactly. In this case, our uncertainties are more than infinitesimal. We have real uncertainties. But we persist with figures that are meant to demonstrate global warming are one such example.
Climate models have uncertainty and the Earth has natural variation…which not only varies year to year, but correlates decade to decade and even century to century. It is really hard to design a figure that shows this in a fair way - our brain cannot deal with the correlations easily.
But we do have mathematical ways of dealing with this problem. The Australian academy reports currently indicate that the models with the effects of CO2 are with 90 per cent statistical certainty better at explaining the data than those without. Most of us who work with uncertainty know that 90 per cent statistical uncertainty cannot be easily shown within a figure - it is too hard to see.
And this leads to problems. Today’s Australian newspaper reports that the warming of the Earth has slowed over the last decade - that is the temperature versus time data shows a leveling off - “Warming data show shades of grey”. Yes! And it - and almost everything else we do in life -is shades of grey. But this does not mean it is not happening, it is just that our understanding is not exact.
Since predicting the exact effects of climate change is not yet possible - we have to live with uncertainty - and take the consensus view that warming can cover a wide range of possibilities, and that the view might change as we learn more.
But the good news is from an economics point of view: there are mathematical ways to deal with uncertainty in policy, to maximise the gain while minimising the pain. Ask Warwick McKibbin here at the ANU, who wrote a book on the subject a decade ago with a colleague, and presented one possible way of best dealing with risk. The book is a good read for those inclined - quite mathematical – and is still as relevant today as it was in the past.
Climate change will continue to be an issue - we can do our best to deal with it now - or we can always pass the responsibility, and the consequences, to future generations.
So grounding ourselves back to the present, the place where people are compelled to act, I had the opportunity to sit next to Jac Nasser – chairman of BHP Billiton at lunch today - and we were discussing some of the biggest problems facing Australian companies and that is skill shortages - inevitably for people who are competent at mathematics.
So if we are complacent, hoping the commodity boom will continue to keep Australia prosperous, not addressing the skills shortage through improving our mathematics skills, we are likely to kill the goose that is laying the golden eggs now, our mining industry.
The future for Australia is bright, but it is not guaranteed. Capitalising on Australia’s opportunities will not just happen, it requires strategic science and education policies that adapt to the changing world. We have to be willing to make major changes to how we go about our business.
But what needs to be done is quite simple. Let’s learn from the OECD’s report. We need to have in place a curriculum that ensures that every Australian child - regardless of what school they go - achieves a level of numeracy that will make them successful citizens, and able to work in a wide variety of jobs. This curriculum needs to allow all students who want to develop a higher level skill set in math, to do so. And this curriculum needs to be taught by teachers with competency in those things we teach.
We are not there yet - too many of our kids leave school without a core numeracy. Too many of our kids - who are able and willing to excel at Maths - are taught by teachers without the level of competency required for the subjects they teach. Solving this skills shortage has to be our highest priority. Our kids cannot afford to have the opportunities lost - that result from having a poor mathematical education - and the nation can ill afford to lose talent which is in such short supply.
Brian Schmidt is a Nobel laureate and Australian National University professor. He delivered this speech at the Australian Mathematical Sciences Institute forum in Canberra on Tuesday 7 February.
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定期存款 Term Deposit (2004-12-20) hick_aus 
楼主:第一教育
发表于 2013-2-18 13:47
发表于 2013-2-18 14:15
