I once asked a mathematician to define the difference between maths and physics. She replied: “If it’s for anything, it isn’t maths.” Stewart disagrees radically. Ultimately, he claims, all maths is practical, although you may have to wait a while to find out bow it applies. He wants to abolish the division between pure and applied maths by insisting that it is all “applicable maths”.

Consequently, most of the book deals with the maths in connection with problems more often labelled as physics or chemistry. Symmetry for him is about molecular stability. The wave equation is about inventing videos and so on. Nature has patterns and regularities; the “job” of mathematics is to track them down, formulate them and use them.

Even with the mystique taken away, there surely remains a mystery about mathematics. Why does it work? Why does this highly abstract formal game, this “unreal” mental construct, deliver accurate descriptions, precise predictions, workable solutions in the “real” world? Or as Stephen Hawking puts it, “what is it that breathes fire into the equations?”

These are the sorts of questions that mathematical illiterates like me want answered. I wish that Stewart had had more space to address them. We would also like to know what mathematicians are up to at the moment, and the nature of their most pressing questions and investigations.

Why do I find the pragmatic approach upsettling? Do I secretly desire the purity of mystical mathematics? I hope this is not the case, although mystery attracts the ignorant. But having encountered the incomprehensibility of Georg Cantor’s concept of the absolute, the frustrating elegance of Kurt Gödel’s incompleteness theorems, or the complex, protracted wrestlings with Pierre de Fermat’s last theorem, I find myself unconvinced by Stewart’s bouncy common sense.

Richard Mabey is an English natural history writer: he is, within this
tradition, a wonderful writer. If he lacks the mystical, high-flown poetry
of, say, Henry Thoreau, he more than compensates for this with the sensitivity
to the social of Izaak Walton. His enthusiasms have a boy-scout quality,
informed and driven by a great accuracy of detail and a shining love for
known landscape and its inhabitants. For Mabey’s wild is the wild of hedgerow,
of enclosed acres and cultivated valleys; not the wild of untracked forest,
untutored square miles and huge sprawling prairie.

Mabey is also a natural historian with a message. Nature is, he claims
in the face of contemporary cliche, an independent creative force: it is
not simply a product of human intervention, creativity or destructiveness.
She, although Mabey studiously avoids such personifications, is self-regenerating,
rises above and through the social, knows her own job better than we do
and could perhaps be left alone to get on with it a little more often.

Mabey’s critique is addressed entirely to ‘conservationist’ ecologists
and greens: he is not, here, challenging the stage beyond – the structuralist
argument that there is no such thing as the ‘natural’, that what we see
is entirely conditioned by who we are and what language we speak. He is
not addressing the theories of social construction (in the 18th century
the English gentleman on his Grand Tour pulled down the blinds of his carriage
so as not to be corrupted by the uncivilised ugliness of the Alps; his 20th-century
equivalent, trained by Romanticism, finds an ecstatic beauty there), but
the simpler issue of people who plant beech trees everywhere and root out
scrubland and believe they are serving a noble cause.

He is of course an ecologist, but his is not the ecology of sentiment
and anthropocentrism; it is a real search for balance and sanity, based
on respect, love and knowledge. It is in his displays of knowledge, the
careful observation of the little – the local scene, the minute topography,
the actual workings of hurricane and Dutch elm disease in this wood, this
valley, this morning – backed up by a long history of looking and studying,
that he is at his best. What to do about replanting the trees of Kew Gardens,
rather than what to do about global warming.

You cannot help but like Mabey, you cannot help but desire to follow
him on his walks. I have never particularly desired to go either to the
Burren in Ireland, nor to the Camargue in France but now, on the strength
of less than 4000 words, I urgently want to do both. Perhaps it is not surprising
that he uses imagery drawn from fractal geometry – that delightfully fuzzy
branch of mathematics which explains the patterns of twigs and the impossibility
of accurate measurement. It offers writers like Mabey a secure base from
which to concentrate on the small.

There is a problem inherent in reviewing all collections of ephemeral
writings, which is what this book is: the reviewer is more or less obliged
to read all through from start to finish, whereas this book should lie at
the bedside for occasional dipping and delight. Read straight through, the
repetitions and contradictions are unfairly obvious.

As both reviewer and general reader, I would have preferred a different
book; one in which Mabey’s argument is clearly followed through and its
force and conclusion spelled out. But this may perhaps be unfair.

I haven’t read any of Mabey’s other books (though I shall be looking
out for them now) but it seems likely that this style, this coming and
going and following his whims, suits his particular writing and his particular
view of landscape better than sustained argument would. However, this approach
might work better without the land-art section – essays on environmental
artists and the connections between human and natural creativity. I can
see how this section could be justified and integrated, but in the absence
of a sustained argument this section feels wedged in, makeweight.

I think his argument – most explicitly put in his immensely helpful
essay on James Lovelock and the Gaia theory, but implicit in almost every
item in the collection – is important. Ecology must not be allowed to become
an uneasy amalgam of nostalgia, psuedo-mysticism and human arrogance. It
must be re-bedded in the actual and in respect for ‘the force that through
the green fuse drives the flower’ (Dylan Thomas).

The serenity and happiness of his mind, the busyness of his eye and
feet make this point far more strongly than a polemic would. This book gave
me many pleasures, but it also made me wildly dissatisfied with myself –
how can I walk the woods and fields of Northamptonshire and see and know
(and therefore, in the proper sense, care) so little?

Sara Maitland is a novelist afflicted with excessive curiosity about
the natural sciences. Her next book, A Big Enough God, about the relationship
between Christianity and contemporary scientific ideas will be published
by Mowbrays this autumn.

Apart from learning all sorts of things to expand the mind and the imagination,
I have also been forced to consider a major cultural problem that we have
in Britain: while science students are supposed to be ‘well-rounded’, arts
students are not. Coming from a decidedly arts background myself, I feel
deprived.

I am not alone in feeling there is something amiss here. In the 1950s
C. P. Snow was writing with concern about ‘the two cultures’. In his new
book about genetics, Colin Tudge analyses the problem:

‘Quite simply science (is) not in the public domain . . . this is far
more true in Britain than in many other countries. In Britain indeed educated
people take pride in not knowing any science. We live in a society dominated
by science and technology, but we do not live in a science ‘culture’. Science
and technology are not treated as a flowering of human creativeness . .
. I want to describe the new science of genetics largely to show just how
interesting it is . . . Science is not a penance. It contains some of the
greatest excitements that any pursuit has to offer: aesthetic as well as
žą˛ÔłŮąđąôąôąđłŚłŮłÜ˛šąô.’

Presumably New ĐÓ°ÉÔ­´´ is not the most important place to raise this
concern as its existence is a major challenge to the dominant culture, but
as readers you might consider doing your bit for a new culture by giving
science books to your less scientific friends and relatives for Christmas.
They must, of course, be the right books.

I have been thinking a good deal recently about what sort of books these
are. I think the clue may lie in two words in Tudge’s last sentence: ‘excitements’
and ‘aesthetic’. Arts-oriented people really do want to know, really are
interested, but we are scared. No one likes feeling stupid; and we feel
stupid if the text is inaccessible or we feel we are being patronised. To
take two negative examples: Gianfranco Vidali’s Superconductivity: The Next
Revolution is scary. Some of this is Cambridge’s fault: it is packaged like
a textbook, not like a good read. But some of it, however, is Vidali’s:
he uses the royal ‘we’ throughout (bad mistake – scientists are distant
enough without them avoiding the first person). On the second page he writes:
‘We require only some background in high school or introductory college
physics.’ Do we indeed? Then I don’t measure up. On a quick skim through
the pages there are far too many complicated-looking diagrams, which convey
no immediate information. I did struggle through and learn a great deal,
but I would not have done so if I had not been invited to review it.

Stephen Hawking’s new collection of essays, Black Holes and Baby Universes,
errs in the opposite direction: a good deal of it seems extremely patronising.
Apart from giving almost everyone a nannyish ticking off (TV producers,
philosophers and the public are all apparently acting irresponsibly) Hawking
reiterates his conviction that ‘each equation I included would halve the
sales’. I am sure that this is untrue (I will come to some books that disprove
it in a minute) and it lets the writer off too easily. This is a slight
and irritating volume: mostly not about science at all, but about Hawking’s
low opinion of the rest of us.

On the other hand, here are three books that seem to me succeed wonderfully
in making different aspects of science exciting. I have already mentioned
Tudge. He really cares that we should all understand enough about genetics
to make responsible decisions about future directions. He begins with Charles
Darwin and ends up with something between a sermon and an appeal. He does
not duck the tricky stuff but shows how you get from anecdote to statistic
to prediction, and why it cannot be done without good mathematics.

There are diagrams that actually help the reader to understand – their
clarity has enabled me, at last, to shift from knowing that DNA came in
something called a double helix, to knowing what that was and why. I found
some peculiarities in his ethical reasoning, but I think that about nonscientific
writers too: and he provides the data which lets me use my own intelligence
rather than insisting that he knows better. Also it feels like a real book
– with a Piero di Cosimo painting on the cover and chapter titles like those
in nonscientific nonfiction.

I have been fond of John Barrow since I discovered his explanation of
Kurt Godel’s Incompleteness Theorums: that if a religion was a belief system
based on non-provable premises then mathematics was the only belief system
that could prove it was a religion. Now fondness has turned to admiration.
Pi in the Sky (great title) is an attempt to introduce a lay readership
to the philosophical questions that underlie mathematics and particularly
the question of why does maths manage to describe the Universe we appear
to have. Is maths invented or discovered? The book goes right back to the
beginning with a historical and anthropological investigation of how numbers
came to be used. Then Barrow works through a lively history of mathematical
concepts, which never ducks the hard bits – including equations – but locates
them so well within the narrative that it is impossible to be more frightened
than fascinated. You swallow the lot eagerly in the desire to learn what
is going to happen next. It’s a model of clarity and interest, full of excitements
and aesthetics.

And finally, the science that seems easiest for us all is natural history.
My current garden-seed catalogue includes a pamphlet called Germination
Times for which degrees in biology and chemistry would seem necessary if
it were about anything except half-hardy annuals which we all know is not
‘science’ but allotments. This case should be exploited as a way into scientific
thought. The Encyclopedia of Land Invertebrate Behaviour is a treasure
trove of delight, wonderfully illustrated, beautifully written and totally
engrossing. In as much as I am most concerned with imaginative fiction,
theology of creation and feeding my son’s curiosity, this book meets all
my needs. It is also glossy and handsome and would make an ideal Christmas
present. It is sad to think how few people will be given it: for this reason
alone we need a more science – oriented society.

Sara Maitland is a writer. Her latest book Home Truths is published
by Chatto & Windus.

* * *

The Engineer in the Garden by Colin Tudge, Jonathan Cape, pp 398, ÂŁ17.99

Superconductivity: The Next Revolution? by Gianfranco Vidali, Cambridge
University Press, pp 165, Pounds sterling 25

Black Holes and Baby Universes by Stephen Hawking, Bantam, pp 189, ÂŁ16.99

Pi in the Sky by John Barrow, Oxford University Press/Penguin, pp 317,
ÂŁ14.95 hbk, ÂŁ7.99 pbk

The Encyclopedia of Land Invertebrate Behaviour by Ron and Ken Preston-Mafham,
Blandford, pp 320, ÂŁ30

Jeremy Bernstein is a rare and precious thing – he is a humane scientist
who can write. This is a little unfair: quite a lot of scientists are humane,
and quite a lot can write, at least about their own field. What is rare
(and even precious) is that he, a physicist whose main job is teaching physics
– rather than poacher turned gamekeeper, so to speak, like many scientific
journalists – can write about a wide range of scientists and sciences, and
broader subjects too, with real illumination.

Bernstein has been a staff writer for The New Yorker since 1961, and
in his articles for this wonderful magazine has developed a style of science
journalism, the scientific profile, in which the personality of the subject
becomes a way for nonspecialists to understand the scientific issues. As
he puts it, ‘The personality serves the message – the science – and not
the other way around . . . Marital infidelity is marital infidelity whether
it is practised by Erwin Schrodinger or your neighbourhood grocer. What
makes Schrodinger special is that he invented wave mechanics and thus transformed
(20th-century) science.’

Perhaps, then, it is not surprising that one of the best pieces in this
collection is about the writer-chemist Primo Levi, who wrote The Periodic
Table and If This is a Man, a book about his experiences in Auschwitz (actually
Bernstein cannot write like Levi could, but then very few writers can write
like Levi could). Bernstein writes about Levi with a real and touching fellow
feeling and argues that the decline in Levi’s last writings were precisely
because Levi stopped being a working chemist and became solely a writer.
It is in this sort of piece that Bernstein’s strengths – his breadth of
knowledge, his journalistic good manners and his relaxed, clear prose –
become most evident. Nor is the Levi essay unique: for example, ‘A Woman’s
Place’, is a discursive biographical note on Sophie Kovaleski, one of the
few female mathematicians of note before this century. It is also a beautifully
written description of her maths and an examination of why women might or
might not be great mathematicians. I’m not sure that I agree with Bernstein’s
conclusions on women, but he informs without bullying.

It is therefore with marked feelings of ingratitude that I have to
say this book does not really work. It is a collection of ephemeral writings,
drawn from a number of sources: The New Yorker naturally, but also an assortment
of other magazines, and unfortunately, too many of the pieces were written
as book reviews. Such writings, although publishers are keen to make them
into books, often feel lightweight when bunched together. Moreover, Bernstein
has a number of pet themes, which although interesting in themselves, become
repetitious when they crop up every twenty pages or so, in ways that they
would not when spread over several years.

The most interesting of these themes, indeed one that needs more thought,
and not just from science writers, is what sort of private biographical
details are appropriate in writings about public achievements. How much
do we need to know about Alan Turing’s homosexuality, Alexander Luria’s
clinical depression or Richard Feynman’s sexual successes? Not a lot, Bernstein
reckons, although he also recognises that there is value in analysing the
moments of childhood in which scientific curiosity was awakened. He is also
interested in discrepancies between Einstein’s autobiography and the historical
facts of his private life.

Once again, I’m not sure that I agree with him entirely (and there is
an annoying complacency in some of his examples), but it is a provocative
issue, key to the sort of writing that Bernstein does, and has a lot to
say to more general journalism and biography. However, due to the format,
we get the same question asked too often and answered too briefly. It is
an inevitable failing of a scrapbook collection, and made this reader, at
least, feel frequently frustrated and bored even in the midst of such interesting
and well-written material.

I shall treat this volume as a sampler and move on – if I can find
them in Britain – to one of the 12 other books of popular science this
fine writer has published.

Sara Maitland is the author of Home Truths, published by Chatto &
Windus.

John McPhee is held to be one of the ten best science writers in the US.
Such a claim has a different sort of status west of the Atlantic than it
would in Britain. In the US – at least since The Sea Around Us became a
bestseller in the 1950s – there has been a highly successful genre of
‘elegantly’ written, serious but nonprofessional, books on science. The
common form requires the personal involvement, in one form or another, of
the writer, and a mix of social observation and scientific fact. These books
also tend to use a great many human analogies, vivid anecdotes and a
special, very American, language of simile and metaphor and jokey ‘modern’
references that are supposed, I think, to make the material feel more
accessible. Stephen Jay Gould is probably the best known practitioner of
this sort of book, while Anni Dillard in Pilgrim at Tinker’s Creek and
Teaching a Stone to Talk merges the genre into ‘real’ literature almost
seamlessly.

Perhaps the deep divide between arts and sciences for which British
education is internationally notorious has alienated British readers from
scientific writing, although the success of A Brief History of Time suggests
that the tide may be turning. Moreover, although the particular writing
style of many of these books would seem entirely appropriate in, say, travel
writing, or even social history, it seems strange and somehow trying when
applied to science (you’re not meant to mix science and triviality).

Nor does it always work: I suspect that many readers in Britain may, like
me, while finding some of Assembling California distinctly tiresome, will
also find other bits pretty heavy going.

‘Above the mantle rock lie the cooled remains of the great magma chamber
that released flowing red rock into the spreading centre. The chamber in
cooling tends to form strata, as developing crystals settle within it like
snow olivine, plagioclase pyroxene snow – but above these cumulate bands it
becomes essentially a massive gabbro shading upwards into plagiogranite as
the magmatic juices chemically differentiate themselves in ways that relate
to temperature.’ And there is quite a lot of this sort of stuff.

But persevere – because there is an extraordinary, and recently discovered,
narrative here. The narrative of tectonic plates – the story of landmass
after landmass rising out of rifts in the mantle, drifting in from the
Pacific, or from somewhere else before there was the Pacific, crunching up
against the west coast of the American continent, squashing, folding up the
Rockies, squeezing past each other, burrowing under each other and
disappearing back into the molten material below the surface. California is
a baby among landmasses, or rather is a litter of baby landmasses still
wrestling, competing, shoving at each other.

Not surprisingly, McPhee does best when the older parts of the narrative
meet human history – the gold rush, the individual geologists who are
working all this out, the civil engineers who are using it. But the book
works (and it does work if the reader is prepared to work too) because the
underlying story is so strange and wonderful and sensible, and McPhee is
clearly enjoying himself as he tells it.

Of course, he is helped immensely by the fact that this is California; and
as he journeys across it from west to east, he gets nearer and nearer to The
Big One – the San Andreas fault and the crazy people who decided to build
cities on it and stay in them. Assembling California is the last part of a
tetralogy – Annals of the Former World in which McFhee has worked his
geological way right across the US – and it was a writerly skill that made
him make the journey east to west thus saving the best bit, the bit everyone
wants to know about, the most dramatic bit, for the finale: when, in 1989,
more than a million apples slumped off the trees in an orchard in under two
minutes, and motorways were buckled, tangled, tossed and people escaped with
their lives or failed to, and then went right on living there. And do so
even though all the geologists know that this was a small earthquake, a
relatively minor release of the massive tension that still exists between
two shifting tectonic plates.

When I can disentangle McPhee’s elaborate and frequently knotted prose, and
can consent to wait to get used to a new vocabulary (I probably learnt more
new words reading this book than in any other week in the past ten years),
the drifting, unstable, complex nature of the Earth beneath me and the
imaginative investigations and speculations of the geologists about it,
excites me enormously. American readers are already more practised in these
grammatical and linguistic leaps. Enough of them must have travelled
McPhee’s long road over the Rockies, across the plain and down to the ocean,
and so can illustrate his tale with their own mental pictures. I lacked this
ability and often longed for a good straightforward map.

Overall, I doubt this book will be a huge success here. But, by chance, this
week I drove down from Central Scotland, right across England to the fens,
and I looked out the window and discovered that I wanted to know the
underlying, the oldest history, of the ground I crossed. I would dearly like
there to be more books dealing at this serious level with major scientific
theories and developments, not just in cosmology and physics (as is becoming
common) but in the stuff that is nearer to hand, like geology.

Sara Maitland is a writer. Her latest book, Home Truths, is published by
Chatto.