Keep your eye on the road (Image: Solstock/Getty)

TOYS, toys, toys. We are deluged with new playthings that make ever more demands for our attention 鈥� many of them digital. How can we focus on anything true or beautiful amid the twitter and chirp of such constant, almost toddler-like demands?

Other writers have excoriated the distractions of ubiquitous technology and advertising. But Matthew Crawford seeks a deep philosophical perspective. He has a background in physics and political science, and is now at the University of Virginia鈥檚 Institute for Advanced Studies in Culture. In The World Beyond Your Head, he explores how we got to what he calls a 鈥渃risis of attention鈥�. His starting onslaught is no less challenging a task than an assault on the 鈥淓nlightenment self鈥�, because, it seems, it is the isolated self that permits distraction.

Immanuel Kant is frequently taken to be the epitome of the 18th-century philosophical Enlightenment, and Crawford blames him for constructing its notion of the self as an isolated being for whom true knowledge can arise only from solo enquiry.

He spreads the blame to the 17th century 鈥� to John Locke, the font of liberal thought, and to Ren茅 Descartes, who said that the only thing he couldn鈥檛 doubt was that there was something, a self, doing the doubting.

Oddly missing is any discussion of another key Enlightenment figure: Adam Smith, who theorised capitalism as an economy of atomised individuals making rational choices in a social vacuum. 鈥淔reedom鈥� and 鈥渃hoice鈥� are the mantras of capitalism. Even though 鈥渨e often assume that diversity is a natural upshot of free choice鈥�, Crawford says, 鈥渢he market ideal of choice鈥� tends toward a monoculture of human types: the late modern consumer self.鈥� As an example, he describes how lobbyists for casino gambling 鈥渢ap into the deep psychology of autonomy鈥� to make it seem that submitting to the engineered attention-grabbing of gambling is a human right.

All this introduces us to one of Crawford鈥檚 key proposals for dealing with the crisis: to shift our focus from the lonesome atomised individual to truly shared attention. The current fashion for the 鈥渨isdom of crowds鈥� is not true sharing, but rather the market mining individuals. As he writes, 鈥渢here is a lot more money to be made as an aggregator of 鈥榗ontent鈥� than as a producer of it鈥�.

聯Crawford proposes shifting our focus from lonesome Enlightenment individual to shared attention聰

Crawford鈥檚 core message is that we should stop focusing on ourselves and move towards true sharing. 鈥淚nvolve your ass, your mind will follow,鈥� he says. He commends to us the 鈥渇low鈥� he feels when riding motorbikes, when his derri猫re is deeply involved in his need to pay attention. He feels it too in his workshop, making motorbike parts and solving problems with others. In particular, he says, we should value education as a face-to-face apprenticeship in the ways of investigating and of making, through attention shared in person. He gives as an example learning to build a pipe organ, with the person who has to repair it in 400 years鈥� time in mind.

You will find a much gentler and more literary exploration of the ills of distraction in the musings of Laurence Scott, who teaches creative writing at Arcadia University in London.

In The Four-Dimensional Human, Scott reaches out not into space-time, but into the 20th-century literary imagination鈥檚 grasping for something outside the mundane three dimensions.

His account of what is becoming of us is often beautiful even if unnerving at times, such as when he evokes the web pages that come alive on anniversaries of their owners鈥� deaths. It is certainly worth our attention.

This article appeared in print under the headline 鈥淭ake a look at your self鈥�

鈥淢assively open online courses are an attempt to have a winner-takes-all economy of teaching鈥�

鈥淔rom composing film music to doctoring: a range of new work will go the way of the assembly worker鈥�

This article appeared in print under the headline 鈥淎 creative accounting鈥�

Counterfeit goods are rampant, but online piracy is a juggernaut (Image: Xinhua News Agency/Eyevine)

There鈥檚 more than one way to handle authorship and copyright in the digital age, according to The Copyright Wars by Peter Baldwin

鈥淣EVER,鈥� I once told a crowd of students, 鈥渢ake advice on copyright from a professor.鈥� The professor next to me bridled. I continued: 鈥淣ot if you want to make a living as a writer or artist. The professor鈥檚 economic interest lies in paying to be published.鈥�

The professor nodded ruefully. They do pay 鈥� especially now that the internet has enabled the rise of online 鈥渙pen access鈥� journals that live entirely from the charges they levy on their authors. An academic鈥檚 reward is in the hereafter 鈥� in future contracts and eventually in tenure.

聯鈥橭pen access鈥� journals live off the charges they levy on authors. An academic鈥檚 reward is in the hereafter聰

Such changes have inspired , professor of history at the University of California, Los Angeles, to produce an epic history of copyright and authors鈥� rights.

Other players brought in by the internet are the corporations that rake in fortunes by copying the works of others 鈥� often without permission and almost always without payment 鈥� and selling advertising alongside them. It is remarkable how little attention Baldwin gives to this, given how they can profit from his keenness on weakening the rights of authors to make a living from a fair share of sales.

The biggest new group the internet brings to the copyright fray, though, are the millions of people who distribute words, images or tunes online with no care for the consequences. Consider the blogger who railed against UK laws that stopped him copying other people鈥檚 music. He was eloquent about it: so eloquent that a newspaper pasted words from his blog into its pages. The blogger strongly objected to being associated with that particular paper. At this point, he turned around and asked for my help in enforcing his copyright.

What particular protection was he seeking? opens: 鈥淐opyright shall be a property right鈥�. It says your creative work is a commodity that you can sell outright. Laws in and are similar.

While the blogger was mildly annoyed that the paper was making money from his words, he was much more distressed at being linked with that particular title. He should have been French. is about authors鈥� rights as individual humans: it is about their right to be identified (or not, as they choose) and to defend the integrity of their works against actions contrary to their 鈥渉onour or reputation鈥�. These are known as 鈥渕oral rights鈥�.

Producers involved in highly collaborative ventures say these get in the way. Scriptwriters are frequently required to waive them, for example, as are regular contributors to 快猫短视频. But for authors generally, and academic authors in particular, identification with their own work and integrity in its use are the only sure means they have to build a career. Such writers cannot be hacks for hire and still do their job. The history of science especially is gritted with tales of when this awkward lesson is forgotten.

Baldwin errs when he says that 鈥渕ost authors assign rights鈥�. Most authors in English-speaking countries keep their rights intact. Elsewhere, authors鈥� rights are generally personal rights and cannot be assigned. But he is to be congratulated for chronicling the development of the authors鈥� rights system so fully: his enormous bibliography is invaluable.

In the 鈥渨ar鈥� of his title, between tradable copyright and personal, inalienable authors鈥� rights, we know whose side Baldwin is on. In reporting lawsuits over Google鈥檚 scanning without permission of 20 million books, he dismisses most authors 鈥� except, perhaps, professors 鈥� as foppish ghosts of a Romantic dream. He declares that making a living from writing is pass茅, and prefers appearances and performances instead.

Jaron Lanier, a pioneer of virtual reality who is on the list of the top 100 public intellectuals, is also a musician. He argued that we should abandon copyright 鈥� until he noticed ( for musicians who had given up on income from publication, spent the money from performances, and now couldn鈥檛 afford healthcare. If you read Baldwin, for balance also read Lanier鈥檚

Baldwin reserves his strongest bile, though, for those pesky Francophone 鈥渕oral rights鈥�. He repeatedly alludes to a supposed connection between moral rights and fascism.

By contrast, in September the Association Litt茅raire et Artistique Internationale (the professional forum for authors鈥� rights) heard from Paul Goldstein, professor of law at Stanford University in California. He suggested that an author鈥檚 autonomy 鈥� expressed in the laws and norms of moral rights 鈥� was now as important a prerequisite of creativity as any promise of cash. He looked forward to an internet that connects authors with their audiences 鈥渋n a bond of reciprocal responsibility鈥�.

For my money, Goldstein鈥檚 is a much more congenial vision than Baldwin鈥檚.

This article appeared in print under the headline 鈥淐opyrights and wrongs鈥�

Thomas Hobbes shared the Jesuits鈥� objection to infinitesimals (Image: Getty Images/DeAgostini)

At stake in the fierce 17th-century debate over a mathematical concept was nothing less than our modern world, says Amir Alexander in Infinitesimal

DID you know that every time you use your cellphone, you strike a blow for republicanism against both monarchy and a fixed Divine Order? Historian Amir Alexander sets out why this is so in his book Infinitesimal, through two tales of struggles against the fundamental tool that makes almost all modern science and technology possible.

This tool is infinitesimals, small slices of continuous measurements that are the basis of calculus. They allow us to discover the areas under curves and to model systems and control them 鈥� offering immense power to shape many facets of our modern world, including cellphone signal processing.

聯Infinitesimals offer immense power to shape many facets of our modern world聰

The first of Alexander鈥檚 tales is of the Jesuits, a Catholic order of priests in personal allegiance to the Pope, founded to stamp out Protestant rebellion. During the early 17th century they strove to suppress the ideas of Bonaventura Cavalieri, a member of the rival order the Jesuats. His use of infinitesimals prefigured the fully fledged calculus of Gottfried Leibniz and Isaac Newton.

To the Jesuits, only a theoretical system built from first principles along logical lines laid down by the ancient Greek mathematician Euclid could provide freedom from paradox and an absolute, approved truth. Pesky new mathematicians like Cavalieri were blatantly assuming the existence of triangles, spheres and so on, then researching them as objects. That way lay free-thinking and challenges to the authority of the Pope.

The 1633 prosecution of Galileo by the Inquisition for insisting that Earth goes round the sun has been better recorded in film and on stage. Alexander connects these two fights 鈥� and a 1651 list of 65 doctrines banned in the Jesuits鈥� colleges, including the atomic theory of matter 鈥� to the political struggles of the Jesuits within the Catholic Church.

His second story is of the dispute between the philosopher Thomas Hobbes and John Wallis, a minister who had been appointed Savilian Professor of Astronomy at the University of Oxford in 1649, mostly because he was a sound Protestant and therefore politically acceptable at the time. Hobbes gained fame for his book Leviathan, in which he argued that the only alternative to a state of nature in which life was 鈥渟olitary, poor, nasty, brutish and short鈥� was absolute monarchy. Though suspected of atheism, Hobbes shared the Jesuits鈥� fear of infinitesimals, defending kingly rather than papal authority.

His opponent Wallis took 鈥渆xperimental mathematics鈥� to extremes, using methods of proof that were patently barking, depending on division by infinity, which is meaningless. Hobbes, meanwhile, died convinced that he had constructed a square with the same area as a circle using only Euclidian methods: he couldn鈥檛 accept that the nature of the number pi makes this impossible.

Those against infinitesimals had ammunition, however. Remember how you puzzled at your teacher鈥檚 insistence that as the number of slices you cut of an object tends to infinity, the sum of the slices approaches the volume of the object. An infinite number of slices with a thickness surely forms an infinitely tall stack? But if they have zero thickness, isn鈥檛 the total zero? And Euclid鈥檚 approach also has appeal, well expressed in the jibe that 鈥渢he proposal is all very well in practice, but it鈥檒l never work in theory鈥�.

Infinitesimal is a gripping and thorough history of the ultimate triumph of the mathematical tool. But it is a shame that Alexander adheres to another doctrinal ban: in Western history, it seems, no mention can be made of Islam as a rival to the Catholic Church. What, for example, was the response to ibn al-Haytham鈥檚 use of proto-infinitesimals in Cairo and Iraq 500 years earlier?

If you are fascinated by numbers, Infinitesimal will inspire you to dig deeper into the implications of the philosophy of mathematics and of knowledge.

This article appeared in print under the headline 鈥淭he smallest subversive鈥�