‘Infinity: A Very Short Introduction’ by Ian Stewart

Infinity is all around us. It helped to send man to the moon and underlines the very basic principles of mathematics, but remains a hugely misunderstood concept.

9780198755234

Picture this: I have a hotel and infinite number of rooms, all of which are occupied. If a new guest were to turn up wanting a room for the night, how could I accommodate them? If you don’t already know the answer to this, then the latest release Oxford University Press’ Very Short Introduction series is sure to be of interest. ‘Infinity: A Very Short Introduction’, by Ian Stewart is, somewhat paradoxically, a quick and simple introduction to what is, quite literally, the biggest subject ever. Intrigued? Read on to find out more.

Let’s get back to my hotel and the matter of how I might accommodate this new and troubling guest. If I had a hotel with a finite number of rooms, the poor chap would be out on his ear, but a hotel with an infinite number of rooms is much more flexible. Instead, I simply need to move the guest in room one to room two, and the guest in room two to room three, and so on, so that each guest has been moved from his current room n, to n+1. Once each guest has been moved, room one will be empty and free to accommodate the new guest.

Confused yet? The hotel’s skills don’t stop here. If in an infinite number of new guests turned up I would also be able to accommodate them. To do this, I would simple need to move the person in room one to room two, and the person in room two to room four, and three to room six, and so on, until each odd numbered room (of which there are an infinite amount) is empty, and ready to be filled by the new guests. I could go on and try to explain how an infinite number of coaches each filled with an infinite number of guests could be accommodated, but my head is starting to hurt.

This hotel, hypothesised by German mathematician David Hilbert in 1924, goes to illustrate the counter-intuitive nature of infinity, by showing that infinity plus one, and infinity plus infinity, are both equal to infinity. More than this, though, Hilbert’s infinite hotel paradox highlights that infinity is paradoxical, so don’t be put off by the paradox of a ‘short’ introduction to a huge subject because when you think about it, illogically it starts to make sense.

Unlike infinity itself, infinity as a concept does have a beginning: it was first hypothesised by Anaximander, a pre-Socratic Greek philosopher from around 580BC. He used ideas of infinity, what he called ‘apeiron’, in the search for the origin of life. Since this time, countless philosophers, theologians, psychologists and mathematicians have delved into the black depths of infinity in search of meaning and explanation.

It might seem strange to think so deeply about a concept that we never physically encounter, but infinity actually comes into play in far more situations than you might imagine. Stewart highlights the example of 1/3 expressed as a decimal – 0.33333 recurring. The recurring number of the decimal goes on forever – it is infinite. In the same way, ideas of space and time are often thought of in terms of infinity, as, of course, are numbers. In fact, infinity has an intrinsic role in all manner of subjects – it underlines the very basis of calculus, has taken man to the moon and is used by mathematicians every day.

Infinity is not a thing, it is a concept, a way of understanding tangible things, and, as Stewart goes to highlight, has a very important role to play. The pattern-seeking nature of the human mind dictates that is preferable, or perhaps easier, to think of certain things as infinite than in attempting to think of a boundary. The mere mention of time having a ‘beginning’ will bring up the question of ‘what came before?’. ‘Nothing’ is an incomprehensible answer.

With ‘Infinity: a Very Short introduction’, Stewart has taken an interminably complex subject, and condensed and contracted it to something reasonably manageable – just reasonably, mind, not entirely, as this is infinity we are talking about. The book introduces puzzles and paradoxes, debunks common misconceptions and explores infinity as a concept in both the natural and theoretical world. The sheer wealth of information is at once fascinating and a little terrifying.

If you’ve ever been struck by the question of what lies at the end of infinity, are baffled by the idea of never ending time or space, or just want to read something that is bound to twist your mind in crazy directions, then this is the book for you.

This review was first published online for E&T magazine

‘Intellectual Property: A Very Short Introduction’ by Siva Vaidhyanathan

From over-the-counter medicines to the corrugated cardboard sleeve on a Starbucks coffee cup, intellectual property law hides in plain sight behind a surprising array of everyday objects, and it doesn’t always have the best of intentions.

9780195372779

Back in December I reviewed ‘The End of Ownership: Personal Property in the Digital Economy’, a book that looks at licensing agreements which come attached to any digital download, and dictate any use, or pleasure, you can take from digital property. If, like me, you love to get into the nitty gritty of what you can and can’t do with information, you no doubt read the review, and bought and consumed the book too.

Where ‘The End of Ownership’ looked at the changing relationship with how we own intellectual property of others, this latest book explores how the very nature of intellectual property has changed over time. ‘Intellectual Property: A Very Short Introduction’ one of the latest great additions to OUP’s mini introduction series, considers  how copyright and patenting laws have changed over from avenues designed to protect and nurture creativity, to tools used for economic gain. That’s right, guys, the reason Amazon want to retain total control over your digital library is because it is in its economic interests to do so.

Author Siva Vaidhyanathan recounts how he first became interested in rules and regulations of intellectual property while working for a large media company that claimed his creative work as its own. As a content producer, Vaidhyanathan saw his work used, reworked and quoted completely outside of the realms of his control. This set the ball rolling for a complex journey into the confusing, and often contradictory, matrix of ownership and creativity.

The story begins with the American music scene, tracing changing dynamics of hip-hop in the 1980s and early 1990s, a time rife with sampling lawsuits inevitably leading to dumbing down of some of the defining characteristics of the music genre. It becomes all the more complex at the turn of the century, with the rise and fall of the first widespread file sharing service – Napster – and the resulting global ‘free culture’ movement of the early 21st century.

This book, though, looks at more than just the relationship between intellectual property and creativity, and how copyright and patent legislation has evolved over time. Rather, it is an approach to understanding your rights as a copyright holder. As Vaidhyanathan says, if you send or receive emails, texts and use social media, you are a copyright holder and more than likely an infringer too. What’s more, if you own a smartphone, tablet or e-reader, and consume digital media therewith, then a substantial portion of the price you pay will go to cover license patents.

You might take for granted that you can buy over-the-counter allergy medicine at a cheap price from your local pharmacy – this wouldn’t have been the case many years ago, when medicine was still covered by patents dictating who could sell it. Patents and copyright licensing are everywhere, from medication on your prescription and CDs in your local HMV, to the unassuming corrugated cardboard sleeve designed to stop you burning your hand on your morning Starbucks flat white. In fact, as Vaidhyanathan points out, Starbucks is just as much an intellectual property company as it is a food and beverage supplier. The coffee company has its own entertainment arm, and produces and sells music it feels will appeal to its clientele. This is just one of the reasons for the eye watering price tag on the aforementioned flat white; all those lawyers don’t come cheap.

Intellectual property is a hugely complicated and confusing theme to try and get your head around, but one thing is clear, it’s all about the money. Intellectual property as it is today is present because there are people who want it to exist. There are companies and individuals with huge economic interests invested in restraining the global movement for standardisation of intellectual property. Copyrights, patents and other laws dictating how property can be used say as much, if not more, about the world in which we live – they do creative content they are designed to protect. Where once intellectual property protection existed to protect and foster creativity, today it has taken on a whole new political, economic and cultural identity.

‘Intellectual Property: A Very Short Introduction’ serves as a wonderfully accessible avenue into a wholly confusing topic, making it another truly spectacular addition to the QUP ‘Very Short Introduction’ series. This is a book for law buffs, experts on rules and regulations, and anyone looking to widen their economic and political understanding of the world – or make a splash at an incredibly specific pub quiz.

This review was first published online for E&T magazine

‘The Industrial Revolution: A Very Short Introduction’ by Robert C Allen

From British feudalism to the Internet of Things, this concise analysis of the Industrial Revolution provides the perfect introduction to one of the most complex times in human history.

51hK1TCIs1L._SX317_BO1,204,203,200_

Look back at the work of any 16th century painter and you will see a life very different to that we live today. Streets were strewn with farm animals and bore witness to all manner of slaughtering, plucking, sheering and bathing alongside horse drawn carts transporting livestock, cloth and grain – a food economy if ever there was one. The land was central to life, with arable plots taken up by livestock and agricultural farming, while towns and cities blossomed along riversides. Craftsmen, placed by the water’s edge for trade, would carve, sand and smooth their wares from metal and wood using hardy hand tools, before selling their goods in local markets. Homes were heated, and food cooked, using wood fires and charcoal, and sanitation left much to be desired.

Fast forward to today and life has moved on somewhat. Hand tools are relegated to those who enjoy gardening and crafts, with production carried out in connected factories, assisted by robotics and autonomous systems. Our houses are heated with oil, gas or renewable sources, and come complete with electric lighting and pristine running water. Most people now live within the confines of the city, which in themselves are vast and busy, with buildings stretching up and out as far as the eye can see. Areas of countryside, rather than offering the gift of life themselves, are set aside for those wishing to ‘reconnect’ with nature and escape the hectic urban life.

So how did we get from one to the other?

The answer lies in the Industrial Revolution, a decisive journey that occurred halfway between life depicted in oil works of the 1500s and today. In this latest Very Short Introduction from Oxford University Press, author Robert C. Allen traces the beginnings of the Industrial Revolution to the humble shores of the British Isles, and analyses the wider global effect of the two centuries of industrial development which helped to shape the course of recent history.

It is a tumultuous story that begins, as with this review, with the wholesome lives of aristocrats, tradesman and labourers in 16th century Britain, where seeds of revolution were sown long before the first cogs of the industrial machine began to turn. The years that followed were a turbulent time, filled with growth, but also contradiction. Alongside the progression man made, was life rife with poverty, unemployment, squalid housing, pollution and protest.

In just over 100 pages, Allen crams 500 years of human development and clears up any uncertainties one might have as to the roots, development and consequences of this Revolution. Despite developments around the world, it was Britain that first saw the ripples of industrialisation, which Allen traces from the English Channel, undulating out into mainland Europe and beyond.

‘The Industrial Revolution: A Very Short Introduction’ is a wonderfully accessible introduction to an incredibly complex period of human history. The revolution itself was made from simultaneous developments across trade, commerce, agriculture, mechanics and economics, and so this introduction, far from being just about the rise of industry, takes into account a breathtaking array of subject matter, but does so within the most manageable of formats. Allen has created another truly fantastic edition to the Very Short Introduction series. This book would make a wonderful addition to any bibliophile’s collection, but would be most ideally suited for those with an interest in industry, British history or international development.

This review was first published online for E&T magazine

Measurement A Very Short Introduction – David J. Hand

9780198779568

Measurement may not sound like the most exciting topic to sink your teeth into as it takes a certain type of person to become excited by a ruler. Yet this book has much more to offer than just a history of centimetres (cm) and inches. Rather, it serves as a brief, but comprehensive glimpse into a social construct that boasts a history that is inextricably bound with the many great leaps forward of civilisation. In Measurement A very Short Introduction, author David Hand traces the origins of measurement back to the beginning of civilised human society, with the birth of agricultural production.

Original units – which relied largely on basic physical objects to quantify length and weight – were of course hugely variable, depending as they did on physical objects. Of course, if there is nothing fundamental leading to the choice of object, other systems of measurement can be adopted. It’s hardly surprising then that a huge number of different systems have been adopted – today we have grams and kilos, pounds and ounces and the dreaded American ‘cup’.

When you take into account the history of units of measurements, measurement itself seems like a fairly vague thing – but this couldn’t be further from the truth. What is a cm? You could say that it is 10mm, or 1/100th of a metre, but how can it be defined on its own? The history is complicated and points toward the need for a unified method of measurement. This became especially important with the rise of scientific experimentation in the 20th century. It’s been a long time coming, but with the birth of the metric system we are getting close, although there are a few stubborn nations who insist on holding on to their outdated ways.

Of course, measurement is not a purely scientific thing, but can also be used to understand social aspects of society. Far from a scientific concept, it spans the entire range of human society, from the purely physical to the wholly abstract. Economic progress can be measured, but it requires a much different system measuring milk or grain – it is something that cannot be conceived with a basic unit of inflation. This, Hand says, is the difference between representative measurement and pragmatic measurement, a wholly different and complex school of thought which is becoming more important to our understanding of society.

Measurement A Very Short Introduction offers the reader a wonderfully accessible route into a hugely complex subject that spans the fields of science, sociology, history and anthropology. From the simple grains and fathoms of old, to GDP, GNI and the modern-day World Happiness Index – the history of measurement has a lot to say about the development of society. Hand has taken a topic that spans almost the whole of human existence and condensed it into a book which the avid reader could easily conquer in an afternoon.

This review was first published on WordPress for E&T magazine