IN OCTOBER 1991, astrophysicists observed something incredible in the skies above , a former weapons-testing facility in a remote corner of Utah. It was a cosmic ray with an enormous amount of energy 鈥� equivalent to the kinetic energy of a baseball travelling at 100 kilometres per hour, but compressed into a subatomic particle. It came to be known as the oh-my-god-particle, and though similar events have been recorded at least 15 times since, mainstream physicists remain baffled by them.

To Jim Carter, a trailer-park owner in Enumclaw, Washington, ultra-high-energy cosmic rays pose no problem. They offer proof of a radical theory of the universe he has been developing for 50 years.

In Carter鈥檚 theory, these rays are photons left over from the earliest stage of cosmic evolution. He calls them 鈥渁pocalyptic photons鈥� and believes that one of them was responsible for the Tunguska event in 1908, in which a mysterious something from outer space flattened 2100 square kilometres of Siberian forest.

Carter鈥檚 ideas are not taken seriously by the physics mainstream. He does not have a PhD and has never had any of his work published in a scientific journal. He has just a single semester of university education, which was enough to convince him that what was being taught in physics departments was an offence to common sense.

In response, Carter went off and developed his own ideas. Five decades on he has his very own theory of everything, an idiosyncratic alternative to quantum mechanics and general relativity, based on the idea that all matter is composed of doughnut-shaped particles called circlons. Since the 1970s he has articulated his ideas in a series of self-published books, including his magnum opus, The Other Theory of Physics.

For the past 18 years I have been collecting the works of what I have come to call 鈥渙utsider physicists鈥�. I now have more than 100 such theories on my shelves. Most of them are single papers, but a number are fully fledged books, often filled with equations and technical diagrams (though I do have one that is couched as a series of poems and another that is written as a fairy tale). Carter鈥檚 is by far the most elaborate work I have encountered.

The mainstream science world has a way of dealing with people like this 鈥� dismiss them as cranks and dump their letters in the bin. While I do not believe any outsider I have encountered has done any work that challenges mainstream physics, I have come to believe that they should not be so summarily ignored.

鈥淭he mainstream science world has a way of dealing with people like this 鈥� dismiss them as cranks鈥�

Consider the sheer numbers. Outsider physicists have their own organisation, the , whose database lists more than 2100 theorists, 5800 papers and over 1300 books worldwide. They have annual conferences, with this year鈥檚 proceedings running to 735 pages. In the time I have been observing the organisation, the NPA has grown from a tiny seed whose founder photocopied his newsletter onto pastel-coloured paper to a thriving international association with video-streamed events.

The NPA鈥檚 website tells us that the group is devoted 鈥渢o broad-ranging, fully open-minded criticism, at the most fundamental levels, of the often irrational and unrealistic doctrines of modern physics and cosmology; and to the ultimate replacement of these doctrines by much sounder ideas鈥�.

Very little unites this disparate group of amateurs 鈥� there are as many theories as members 鈥� except for a common belief that 鈥渟omething is drastically wrong in contemporary physics and cosmology, and that a new spirit of open-mindedness is desperately needed鈥�. They are unanimous in the view that mainstream physics has been hijacked by a kind of priestly caste who speak a secret language 鈥� in other words, mathematics 鈥� that is incomprehensible to most human beings. They claim that the natural world speaks a language which all of us can, or should be able to, understand. Rather than having their dialogue with the world mediated by 鈥渆xperts鈥�, NPA members insist that they can commune with it directly and describe its patterns in accessible terms.

Regardless of the credibility of this claim, it is sociologically significant. In their militantly egalitarian opposition to what they see as a physics elite, NPA members mirror the stance of Martin Luther and other pioneers of the Protestant Reformation. Luther was rebelling against the abstractions of the Latin-writing Catholic priesthood, and one of his most revolutionary moves was to translate the Bible into vernacular German. Just as Luther declared that all people could read the book of God for themselves, so the NPA today asserts that all of us ought to be able to read the book of nature for ourselves.

And just as Luther didn鈥檛 reject the basic tenets of Christianity, outsider theorists do not reject science: they believe that it provides the right tools to reveal the majesty of our world. But they insist that the wonders of science be available to everyone.

It is here that we can find common ground with them. Many of us who love science would probably agree that one of its functions is to enable us to feel 鈥渁t home in the cosmos鈥�, as theoretical biologist Stuart Kauffman of the University of Vermont in Burlington famously put it. Outsider physicists don鈥檛 feel at home in a universe described by the tensor equations of general relativity or the gauge symmetries of string theory. They feel alienated by it.

While we may not agree with the answers outsiders give, none of us should be sanguine when some of the greatest fruits of science are unavailable to most of humankind.

I WAS ten when I had an almost mystical experience in a maths class, right after my teacher revealed to us the secret of circles 鈥� the number known as pi. I had grasped that pi, and hence true circles, were purely mathematical entities. Yet I had seen hundreds of almost-circles, both natural and artificial: in the shape of the sun and moon, in the eyes of cats, the faces of clocks, the wheels of cars. How could an abstract entity play such a prominent role in the real world? Just how did mathematics and physical reality mesh?

How delightful to encounter, thirty years later, a book devoted to these very questions. More so, since Ernest Zebrowski鈥檚 A History of the Circle is both charming and genuinely insightful.

Zebrowski introduces us to the cultural history of the circle from the beginning, through its incarnations in the wheel, the roller and pulley. It has been the backbone of many technologies 鈥� from the ingenious methods that built the Egyptian pyramids through clocks and gears and on (more abstractly) via the cycling of radio waves to modern telecommunications. Investigations of the circle and its mathematical cousins, such as elipses, have contributed enormously to our scientific understanding of natural phenomena, from rainbows to the Solar System and the quantum properties of atoms.

Yet nowhere in the physical world are true circles realised 鈥� coins have ridges around the rims, tyres are slightly squashed at the bottom. Even a computer can鈥檛 draw one. 鈥淭his book is about something that doesn鈥檛 physically exist,鈥� Zebrowski bluntly declares.

Are true circles, then, mere figments of our imaginations? The question has immense significance because it applies to all the maths we 鈥渄iscover鈥�. Zebrowski concludes that like all mathematical entities, circles inhabit an imaginary netherworld.

But just as we cannot see or touch a true circle 鈥� only imagine one 鈥� neither can we see or touch neutrinos, dark matter, or even radio waves. Like true circles, these scientific 鈥渄iscoveries鈥� also depend far more on mathematical arguments than on direct sensory experience, notes Zebrowski. Given the increasingly indirect nature of much scientific 鈥渙bservation鈥� 鈥� particularly in high energy physics 鈥� Zebrowski predicts ever more 鈥渄iscoveries whose relationships to objective reality are tenuous at best鈥�. And he thinks this irrestible rise of mathematics has its downside, too 鈥� increasing 鈥渙ur risk of confusing the essence of the physical universe with its mathematical messengers鈥�.

If, as Zebrowski seems to be suggesting, that 鈥渆ssence鈥� is something other than mathematics, one is left with the puzzle of why maths works so well in describing the physical Universe. Why does so much maths begin as a purelyintellectual inquiry, only to find applications years later 鈥� group theory, for example, in nuclear physics, and Riemannian geometry in Einstein鈥檚 general relativity?

Here Zebrowski prefers biology to complex philosophy or mysticism. From sharpening flints to the trajectories of neutrinos, all physical events take place in time and space, and Zebrowski suggests that evolving an intuitive sense of geometry must have been important to the survival of our Stone Age ancestors. Not only has the brain evolved to invent mathematical systems that conform to physical reality, he suggests. It may not even be capable of dreaming up alternative schemes.

Whether there are limits to what we can know about physical reality through maths, however, remains, as Zebrowski notes, one of the great philosophical riddles.

AS PHILOSOPHER Mary Midgley has noted, the fantasies of 鈥渢he scientific
imagination鈥� are markers of deep psychological currents circulating in our
society鈥攔eflecting not only what we see as possible, but, perhaps more
tellingly, what many see as 鈥渄esirable鈥�. In How We Became Posthuman, N.
Katherine Hayles examines the fantasies emerging from the matrix of cybernetics,
artificial intelligence and the fledgling technologies of cyberspace. In
particular, Hayles explores the cybernetic desire to 鈥渇ree鈥� information from the
ballast of materiality鈥攚hich reaches its apotheosis in the current fantasy
of achieving immortality by uploading ourselves into cyberspace.

At a time when fallout from the 鈥渟cience wars鈥� continues to cast a pall over
the American intellectual landscape, Hayles is a rare and welcome voice. She is
a literary theorist at the University of California at Los Angeles who also
holds an advanced degree in chemistry. Bridging the chasm between C. P. Snow鈥檚
鈥渢wo cultures鈥� with effortless grace, she has been for the past decade a leading
writer on the interplay between science and literature.

Now, she turns her attention to the rich flux between the
cybernetic/informatic sciences and the wider cultural milieu. It is a flux that
she shows is reconfiguring not only our imaginations but our very notions of
what it means to be human. But the 鈥減osthumans鈥� of her title refer not just to
the fantastical and virtual bodies envisioned by science fiction writers and
techno-extremists such as the Extropians, who believe human intelligence and
technology will allow life to expand indefinitely. Hayles also asserts that even
without prosthetic enhancements we are all becoming posthuman, because the very
idea of the liberal humanist 鈥渟ubject鈥� is being profoundly challenged by new
technologies.

The basis of this scrupulously researched work is a history of the cybernetic
and informatic sciences, and the evolution of the concept of 鈥渋nformation鈥� as
something ontologically separate from any material substrate. Hayles traces the
development of this vision through three distinct stages, beginning with the
famous Macy conferences of the 1940s and 1950s (with participants such as Claude
Shannon and Norbert Weiner), through the ideas of Humberto Maturana and
Francisco Varela about 鈥渁utopoietic鈥� self-organising systems, and on to more
recent conceptions of virtual (or purely informatic) 鈥渃reatures鈥�, 鈥渁gents鈥� and
human beings.

Once information had been 鈥渄isembodied鈥� and 鈥渄econtextualised鈥� (a move which,
Hayles shows, did not happen without resistance), the stage was set for a
radical re-evaluation of both humans and machines. On the one hand, a path was
laid for the development of artificial intelligences, or human-like computers;
on the other, humans could now be seen as computers in biological form. At the
heart of both visions鈥攚hich Hayles explores in literary texts as well as
scientific theories鈥攊s the belief that pure information (independent of
any material form) is the key to selfhood, both human and machine. It is just
these ideas of disembodied selfhood and dematerialised information that Hayles
wishes to challenge, and which she ultimately refutes.

Every major US academic press has been churning out such texts, and although
this is not the best I have read, a number of the entries make this volume well
worth the price. Aside from Hayles, a literary theorist at UCLA who also holds
an advanced degree in chemistry and reprises some ideas from her
Posthumans, here are many of the usual suspects: California cyber-guru
Michael Heim, MIT鈥檚 cyber-architectural theorist William Mitchell, and new-media
artists Carol Gigliotti and Brenda Laurel. Particularly fine essays are also
contributed by Erkki Huhtamo, who gives a quirky historical analysis of shifting
attitudes towards automated machines and computers; and the always insightful
Lev Manovich, who discusses the possibilities of 鈥渄igital cinema鈥�.

Like high-tech cousins of Rosie the Riveter, women in the 1940s had been
encouraged by government campaigns to develop science and engineering skills,
and many rose to the challenge. Women scientists were invited to fill the vacuum
created as men were called away from academic and civilian posts to contribute
to the war effort. Worse was to come. As the war ended, academic institutions
all over the country quickly shifted their priorities.

The rule forbidding institutions from hiring relatives of faculty members
also worked strongly against female scientists. Many were married to scientists,
and guess who had to step back? Even first-rate women, such as future Nobel
physics prizewinner Maria Goeppert-Mayer, often had to be content with
unofficial or lowly 鈥渁ssistant鈥� posts.

Rossiter鈥檚 book, scrupulously researched and chock-full of statistical and
anecdotal data, is essential if depressing reading. It does end on a note of
optimism: the dawning of the women鈥檚 movement in the early 1970s. You can look
forward to happier times in Volume 3.

WE CAN measure the velocity of a planet through the Solar System or of a
cannon ball across a battlefield. But we can only do so because the concept of
velocity was 鈥渋nvented鈥�. And this happened in the 17th century, when scientists
such as Galileo and Descartes gradually developed a new mechanistic philosophy
of nature.

One of Michael Blay鈥檚 many fine achievements in Reasoning with the
Infiniteis to make us realise how velocity, and later instantaneous
velocity, came to play a vital part in the development of a rigorous
mathematical science of motion鈥攖he major triumph of the scientific
revolution. From this gradual mathematisation of motion grew the belief that the
whole of physical reality could be subdued under a mathematical umbrella.

Central to Blay鈥檚 tale is the problem of infinity鈥攐r more particularly,
of the infinitesimal. From the time of the Greek philosopher Zeno, the issue of
infinities and infinitesimals had been central to the discourse about motion.
But the paradoxes raised by the philosophical logic which showed that Zeno鈥檚
arrow could never reach its target stymied a mathematical science of motion.
Theologians joined philosophers in believing the infinite was
inexplicable鈥攚hich proved an immense psychological barrier to new ideas.
Blay shows how a barrage of new mathematical techniques, culminating with
Leibnitz鈥檚 and/or Newton鈥檚 invention of the differential calculus, overcame this
resistance.

This stunning success came at a price. With the new techniques, the Galilean
project of mathematising the world moved from the firm foundations of geometry
to the dubious sands of differential calculus鈥攚hose meaning remained
shrouded in mystery. For while infinitesimals made calculus work, their
ontological status remained dubious at best: no-one understood what they
represented. But, as Blay notes, this has set the tone for physics ever
since.