Is That A Big Number? is now a book (Oxford University Press July 2018).
Hear Andrew being interviewed by Jim Stein for New Books Network:
Available from all good booksellers, including:
From the cover blurb:
Is That a Big Number? is, first of all, a celebration of a numerate way of understanding the world. It shows how number skills help us to understand the world close at hand, and how the same skills can be stretched to demystify and even embrace the bigger numbers that we find in the wider contexts of science, politics, and the universe.
Written in a light and engaging style, this book does have a serious motivation. A responsible citizen is an informed citizen, and that requires a level of numeracy that most of us struggle to achieve. This has created a schism between the citizen and the 'experts', to the detriment of all. Andrew Elliott's underlying aim is to help to address this by extending the reach of practical numeracy.
Here's an idea of what the book contains:
Numbers are important. They arise naturally from daily life, but when they become large, we all struggle to keep our grip on them. This book celebrates the numbers we encounter in life, and points to five techniques of thinking about big numbers to help us understand them better.
Use memorable - and memorised - numbers for instant comparisons and yardsticks to help you put big numbers in context.
All about counting and things that can be counted. It starts simply enough: one, two, three ..., just like a nursery rhyme. But as the numbers grow bigger we stop being able to count in this way and we need to find new techniques. We count in bundles, in chunks. We start estimating and making models. And when we start trying to discover how many fish in the sea or stars in the sky, we count it a success to even get the order of magnitude right.
Numeracy is not maths, it's about connecting the abstraction of numbers to the real world around us. We are not equipped by nature to be calculating creatures, and our native numerical capabilities are limited. But we enlist the cultural skills of memory and imagination, and process and reasoning to develop ways of working with numbers in our daily lives. Numeracy and literacy are intimately entangled, and our language shows this. Somewhere around 1000, however, we lose this connection and we start to feel out of our depth.
Using imagination to picture the number in a context that allows mental comparisons.
Measurement is counting with units attached, and the most fundamental measurements we make are those to do with length. From ancient times we have measured with body parts - fingers, arms, feet - but the metric system is global: a metre is one ten-millionth of the distance from pole to equator. Sport loves numbers and especially distances: measures for playing fields, for equipment, for record jumps. The chapter also covers heights of buildings, lengths of journeys, roads, railways and rivers. Understanding these numbers gives scale to the world.
Breaking the big number down into smaller parts and working with the parts.
Measurement of time has been a spur to technology for thousands of years, and we've had to struggle to accommodate the natural cycles of the Earth and the Moon to make useful clocks and calendars. Some of the big numbers that are hardest to grasp are the numbers that describe the Earth's deep past: after all recorded history is barely one-millionth of the Earth's lifespan. An Even Briefer History of Time gives a numbers-based view of prehistory and ancient history.
Areas and volumes increase much faster than linear measures, and this throws off our ability to accurately gauge the numbers involved. Historically, land was measured by how much we could plough in a day, but when we start measuring bigger areas we reach for other measures, such as "the size of Wales". And when we're shipping valuable liquids (such as oil and alcohol) we've developed all sorts of ways of measuring their volume.
Bringing numbers down to size, by expressing them as a proportion of some base.
Trading and weighing go hand in hand. From the smallest units, like the grain, up to the largest, like the ton, systems of weighing have been linked to the need to establish common understanding for the purpose of trade. But like volumes, weights increase so much faster than lengths, that we can find the numbers becoming very big, very quickly.
Through recent centuries, speed has been virtually synonymous with progress. But do you know your orbital velocity from your escape velocity? And will the Bloodhound SSC project really smash the world land speed record? (and how fast IS the world's fastest drummer?)
Time to review and to reflect. The distribution of numbers "in the wild" shows some curious features. It starts to seem that when we think about big numbers it might be more helpful to think about proportions and ratios rather than absolute differences.
Dealing with numbers of widely different scales by measuring working with a scale based on proportionate variation.
The numbers of science start stretching our capacity for thinking about big numbers. How high is the moon? How big is our solar system? Our galaxy? The whole of the observable universe? These astronomical numbers stretch our numerical abilities even further. How can we possibly begin to form any sort of intuition about these numbers, any sort of feel for what they mean?
Measuring energy is problematic, perhaps because "energy" as a formally unified concept appears only quite recently in human history. So, while in theory the joule underlies them all, in practice we have different schemes for measuring energy of different kinds: electrical, food energy, explosive energy, fuel energy. This makes comparisons hard to do and sometimes surprising in outcome.
We live in an information-rich society, and measuring information has become important in many ways. It's also one area where we have lived through a period where the everyday measurements of data storage has progressed from kilobytes to Megabytes, Gigabytes, Terabytes, Petabytes and beyond.
This is not a book of mathematics. But the mathematical field of combinatorics involves counting combinations and permutations, and this gives rise to some very big numbers indeed, and some of these are very important to understanding what problems can and cannot be solved in a practical sense by computer techniques.
They say money makes the world go round, but how do we measure money? Older measures of money were related to weights, particularly of silver and gold, but now money has no solid connection to physical assets: all currencies are relative, and inflation makes our measurement of wealth and income date-dependent. But these are important numbers and few of us have a good understanding of the really big money numbers, national earnings and budgets, are measured. That's where A Bluffer's Guide to National Finances comes to your aid.
Over the last couple of centuries, the population of the world has soared. We're more than 7 billion in number, and that's expected to grow through the rest of the century. But it does seem that we reached a point where the population growth rate is tailing off. Is there space in the world for all of us? What about the other animal species that are driven into smaller and smaller habitats?
Sometimes averages are misleading, and we need to look at how to measure variability and inequality in data. It seems paradoxical but most people earn less than the average. How do we make sense of such measures? If measurement is critical to setting targets and measuring achievement, in public policy as in other parts of life, what should we measure? What have people been measuring, and what do the numbers show?
In a world of ubiquitous computing, do numbers still count? In a post-fact world, we need ways to detect deception and find solid ground. If we are better able to understand the numbers that describe the world, then this will help us establish a firm footing and guide us to know when we're being misled. Yes, numbers count.