Monthly Archives: March 2014

Optimising the future with mathematics

Geoff Prince, Australian Mathematical Sciences Institute

AUSTRALIA 2025: How will science address the challenges of the future? In collaboration with Australia’s chief scientist Ian Chubb, we’re asking how each science discipline will contribute to Australia now and in the future. Written by luminaries and accompanied by two expert commentaries to ensure a broader perspective, these articles run fortnightly and focus on each of the major scientific areas. Today, we add mathematics to the mix.

Mathematics is an absolutely critical part of our future – and we can maximise its impact for the public and private good over the next 11 years if we take the opportunity now.

It is the multidisciplinary and universal nature of mathematics which makes this true: multidisciplinary because of its vast scope and universal because of the effectiveness of its processes.

In some fields it plays a supportive role and in others, the lead. I will describe a lead role which will be crucial to achieving the sort of economy we want: the optimisation of public and private sector enterprise. (I will touch on statistics and its role in data analysis only in passing as my esteemed colleague Terry Speed will cover it later in this series.)

Charles Darwin summed up the deep importance of mathematics when he said

Mathematics seems to endow one with something like a new sense.

Mathematicians do not have a monopoly on this extra sense. Broad mathematical capability across the community underpins most qualities identified in the aspiration for 2025. Bankers, nurses and engineers competently practise various forms of mathematics on a daily basis.

Today’s 12-year-olds entering secondary school will be 2025’s young graduates.
After the slide in the performance of our 15-year-olds exposed in the latest Programme for International Student Assessments (PISA) results, it’s not clear that they will enjoy the same broad mathematical capability as today’s 23-year-olds.

The Australian Mathematical Sciences Institute’s (AMSI) own aspiration for 2025 is to lift the percentage of secondary maths classes taught by qualified maths teachers from an appalling 66% now to 100%.

We have serious work to do here just to maintain the status quo, but we must also be prepared to deal with the new quantitative and qualitative challenges thrown up by this rapidly changing world – and to do that, we must be more agile than we are at present.

Getting practical about mathematics

Biology is a case in point. The slow uptake of mathematics and statistics in the university biology curriculum hampers our progress despite the demand for mathematically capable specialists at the research frontier.

The lesson here is to connect mathematics and biology in our schools, two disciplines which have not traditionally been close (notwithstanding Darwin’s observation). Maths is meeting the biosciences in the 21st century much as maths met physics in the 20th, and we must communicate this through the curriculum – not leave it to Brian Cox, Simon Singh, Facebook and Twitter.

We need our ‘mathematical sense’ or we risk ending up with The Blind Leading the Blind (Pieter Bruegel the Elder, 1568).
Wikimedia Commons, CC BY

The advanced mathematics that the discipline itself practises loosely splits into

  1. theoretical mathematics: developed without an immediate view to external application. It is the deep intellectual nature of theoretical mathematics which attracts many to the discipline (think of the Clay Millennium problems).
  2. applicable mathematics: focused on practical benefit on various time scales. It is applicable mathematics which most directly, but not exclusively, impacts on our aspirations for 2025.

Many of any of us move freely between the two and history shows that the multidisciplinary capacity of mathematics depends critically on the health of the discipline proper. The use of 19th and 20th century differential geometry in 21st century computer graphics is a striking example. This pointed observation is aimed at the managements of our universities!

The word cloud below shows some public, private and research enterprises, all contributing critically to where we will be in 2025 and all employing or engaging with research-trained mathematicians and statisticians.

Wordle

Mathematicians’ roles are increasingly important in a world addicted to progress, and they are multidisciplinary in nature – statisticians work with retailers to refine and analyse their loyalty programs and mathematicians work with banks to manage financial risk and with the hospitals to manage emergency ward workflows.

We make a fundamental contribution to the growth of knowledge based industries and to the smart operation of the natural and primary resource sectors. Unfortunately we don’t communicate this very well, especially to students and their parents, but we are making a start.

The practice of this applicable mathematics can be broken into support roles and lead roles. Roughly speaking the support roles involve the practice of existing sophisticated mathematics and the lead roles involve active research:

  • computational mathematics plays a lead role in industrial, biological, economic and environmental modelling, such as in the increasing accuracy and sophistication of climate change models
  • bioinformatics plays a lead role in genetics, creating algorithms to analyse genomic data to expose genetic markers for disease
  • optimisation should play a lead role in both making the Australian economy competitive in 2025 and in improving our national well-being.

Optimising optimisation

Broadly speaking, the mathematical field of optimisation involves determining an optimal scenario (relative to some criteria) among a collection of alternatives.

The determination of the most efficient route between two locations, where “route” and “location” can have many meanings, or the most economical use of resources in production processes. Optimisation problems can involve thousands of variables and minimise or maximise many “objective functions”.

It sounds dry, but it cries out “productivity growth!” and “competitive advantage!” and, in times of emergency, “lives saved!

Darwin would certainly agree that optimisation is in his “new sense” category.

Australia is getting better at optimisation, from traffic management to mining to aircraft scheduling, but it’s patchy. The defence forces are very good at it, in part due to the work of the Defence Science and Technology Organisation (DSTO), as well as the CSIRO, NICTA, IBM and some of the universities.

Adrianne Behning Photography/Flickr, CC BY-NC-ND

The health sector is not uniformly good at optimisation, nor are our public transport systems.

Small to medium enterprise is not good at it at all. We are babes in the woods compared to countries such as Germany and the US for whom optimisation is worth billions.

The really smart way to optimise infrastructure is to build optimality into the design. We almost never to do this – we usually optimise as an afterthought, if at all.

But one shining Australian example of optimisation in design is the work of business analytics and optimisation company Biarri Commercial Mathematics on the National Broadband Network (NBN) – work so good that they are one of six global 2014 finalists for the prestigious Franz Edelman Prize.

The mandating by government of optimisation integral to design for significant public and private infrastructure projects would have a transformative impact on the Australian economy. It would not only boost productivity but build in competitive advantage and contribute to a sustainable future.

Optimisation would become part of the economic culture at all scales.

By keeping the bureaucracy to a minimum this measure would encourage the growth of dynamic companies like Biarri and draw on the capacity of CSIRO, IBM, NICTA and the universities, all of whom would be able to tender for the design work.

It would strengthen the mathematical sciences and thrust us, sure-footed, towards 2025 and beyond without fear of falling into the ditch of mathematical ignorance.


Nalini Joshi, Professor of Mathematics at the University of Sydney

Mathematics is a universal language that unlocks innovation by abstracting a problem to reveal patterns that answer the crucial questions. The key to Australia’s future competitiveness and security lies in continually creating and adapting mathematical representations of the real world.

Mathematical truths make a complex world more comprehensible and manageable; they are intertwined with efficiency and innovation at all levels of the economy.

lytfyre/Flickr, CC BY-NC-SA

Mathematics can show us how to minimise traffic snarls in our cities, cut costs in a complex network of rail transportation, avoid congestion on the internet, produce innovative designs in optical lenses, weigh costs and benefits of environmental policies and optimise a small business plan.

Mathematics can create new and better Australian industries. It is now central to fundamental questions of nature, life and health.

How does genomic information lead to development and better health in early life? How can the resolution of medical images be improved while reducing their file size? How can mathematics be used to create a safer regulatory framework for financial markets?

The more technologically sophisticated a society becomes, the more critical its need for mathematical thinking. The pathways towards economic diversity and opportunity are paved with mathematics.


John Rice, Honorary Professor of Mathematics at the University of Sydney

A smart economy depends on mathematical skills but you would hardly know it. Mathematics in practice is often not recognised as such, and unrecognisable in terms of school and undergraduate mathematics. This is the great failure of mathematics education.

The greatest contribution that the discipline of mathematics could make to Australia’s smart economy is to remedy that.

The remedy concerns approach as well as content. Mathematics as it is practised, in research and professional occupations, requires thought, creativity, judgement, questioning and problem solving. An economy based on production lines might not require these skills as a matter of course, but a knowledge and innovations-based economy does.

queensu/Flickr, CC BY-NC-ND

Current mathematics education, in schools and universities, is satisfied with programming students to carry out certain mathematical processes, and assessment rewards students who can calculate everything even if they understand nothing.

It’s more like preparing for a production line than a knowledge based economy.

The mathematics discipline seeks a remedy in improving the knowledge base of those teaching mathematics. However, “upskilling” teachers with “more of the same” will not deliver mathematics in the form that a smart Australia needs.

We need mathematics “to be taught more like it is done” by those engaged in it, in both the innovations economy and research. This is a cultural change that involves the discipline itself, one that must be mainstreamed into school and university systems.

Without this, the connection between mathematics and the economy will remain dubious in the public mind, and mathematics will remain hamstrung in achieving its proper influence and delivering its benefits to a 21st century Australia.


This article is part of the Australia 2025: smart science series, co-published with the Office of the Chief Scientist.
Further reading:
Australia’s future depends on a strong science focus today
Physics: a fundamental force for future security
Proteins to plastics: chemistry as a dynamic discipline
Australia can nurture growth and prosperity through biology
A healthy future? Let’s put medical science under the microscope
Groundbreaking earth sciences for a smart – and lucky – country
To reach for the stars, Australia must focus on astronomy
Marine science: challenges for a growing ‘blue economy’
Building the nation will be impossible without engineers
Australia’s got ICT talent – so how do we make the most of it?
Agriculture in Australia: growing more than our farming future

Geoff Prince, Director and Professor, Australian Mathematical Sciences Institute

This article was originally published on The Conversation. Read the original article.

The science that makes us spend more in supermarkets, and feel good while we do it

Graham Kendall, University of Nottingham

When you walk into a supermarket, you probably want to spend as little money as possible. The supermarket wants you to spend as much money as possible. Let battle commence.

As you enter the store your senses come under assault. You will often find that fresh produce (fruit, vegetables, flowers) is the first thing you see. The vibrant colours put you in a good mood, and the happier you are the more you are likely to spend.

Your sense of smell is also targeted. Freshly baked bread or roasting chickens reinforce how fresh the produce is and makes you feel hungry. You might even buy a chicken “to save you the bother of cooking one yourself”. Even your sense of hearing may come under attack. Music with a slow rhythm tends to make you move slower, meaning you spend more time in the store.

Fresh Produce at a Supermarket.

Supermarkets exploit human nature to increase their profits. Have you ever wondered why items are sold in packs of 225g, rather than 250g? Cynics might argue that this is to make it more difficult to compare prices as we are working with unfamiliar weights. Supermarkets also rely on you not really checking what you are buying. You might assume that buying in bulk is more economic. This is not always the case. Besides, given that almost half of our food is believed to be thrown away, your savings might end up in the bin anyway.

Strategies such as those above get reported in the media on a regular basis. Mark Armstrong analysed retail discounting strategies for The Conversation last year, for example, and the Daily Mail recently published a feature on making “rip offs look like bargains”.

You might think that awareness of these strategies would negate their effectiveness, but that doesn’t appear to be the case. It would be a strong person that does not give way to an impulse buy occasionally and, for the supermarkets, the profits keep flowing.

Product placement

There are marketing strategies which you may not be aware of that also have an effect on our buying habits. Have you ever considered how supermarkets decide where to place items on the shelves and, more importantly, why they place them where they do?

When you see items on a supermarket shelf, you are actually looking at a planogram. A planogram is defined as a “diagram or model that indicates the placement of retail products on shelves in order to maximise sales”.

Planograms in action.
lyzadanger

Within these planograms, one phrase commonly used is “eye level is buy level”, indicating that products positioned at eye level are likely to sell better. You may find that the more expensive options are at eye level or just below, while the store’s own brands are placed higher or lower on the shelves. Next time you are in a supermarket, just keep note of how many times you need to bend down, or stretch, to reach something you need. You might be surprised.

The “number of facings”, that is how many items of a product you can see, also has an effect on sales. The more visible a product, the higher the sales are likely to be. The location of goods in an aisle is also important. There is a school of thought that goods placed at the start of an aisle do not sell as well. A customer needs time to adjust to being in the aisle, so it takes a little time before they can decide what to buy.

You might think that designing a good planogram is about putting similar goods together; cereals, toiletries, baking goods and so on. However, supermarkets have found it makes sense to place some goods together even though they are not in the same category. Beer and crisps is an obvious example. If you are buying beer, crisps seem like a good idea, and convenience makes a purchase more likely. You may also find that they are the high quality brands, but “that’s okay, why not treat ourselves?”

This idea of placing complementary goods together is a difficult problem. Beer and crisps might seem an easy choice but this could have an effect on the overall sales of crisps, especially if the space given to crisps in other parts of the store is reduced. And what do you do with peanuts, have them near the beer as well?

Supermarkets will also want customers to buy more expensive products – a process known as “upselling”. If you want to persuade the customer to buy the more expensive brand of lager, how should you arrange the store? You still need to stock the cheaper options, for those that are really are on a budget. But for the customers that can afford it, you want them to choose the premium product. Getting that balance right is not easy. My colleagues and I are among the researchers striving to develop the perfect algorithm taking into account size, height and depth of shelves, to direct customers to the right product, at the right time.

Shoppers won’t always obey the science, but these techniques are retailers’ most effective tools in the fight for our weekly budget. The battle between supermarkets and their customers continues.

Graham Kendall, Professor of Operations Research and Vice-Provost, University of Nottingham

This article was originally published on The Conversation. Read the original article.