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Authors: Tim Robinson

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The popularizations of these theories – paradoxically, many of them pioneered in an institute of Santa Fé that is historically downwind from Los Alamos – are among the most liberating texts I have read in recent years. But at a much earlier stage of my life, and in connection with orders of existence one or two steps above and below those just considered, I struggled with those two great intellectual constructions that stand like the Pillars of Hercules at the opening into twentieth-century physics: relativity and
quantum
theory. It must have been in my middle-school years that I heard Fred Hoyle’s BBC talks on the new cosmology; I
remember
vividly his explaining that the universe is expanding like the surface of a balloon being inflated, of which ‘the radius, of course, is Time’, and I was particularly struck by that ‘of course’, which made me want to be on such first-name terms with Time. I read
and persuaded myself that I followed Einstein’s popular book on relativity, and at least I could appreciate and be amazed at the fact that the famous equation
E
=
mc
2
falls out from some
comparatively
simple mathematics with heart-stopping suddenness. (It expresses the equivalence between energy and mass,
c
being the speed of light, which is an enormous number, so that
c
2
is, one could say, enormously enormous, implying that a stupendous amount of energy can be derived from a very little mass, as had been demonstrated a few years earlier when two cities and their inhabitants were deleted by a few grams of
uranium and
plutonium
, and as we can feel every day from the sunshine on our faces, the sun having been pouring out that flux of radiant energy not just towards the tiny distant dot of the Earth but into all the vastness of space surrounding it, day in day out for millennia, without appreciable loss of substance.)

One or two images from Einstein, in particular that of the observer sitting on a rotating disc as a ray of light passes, which I associate with Tenniel’s illustration of the Caterpillar smoking his hookah on a mushroom, still lie in a cupboard of my mind and come to light now and again. The curvature of spacetime as the gravitational effect of mass, and the speculation that our universe may be finite and yet have no bounds, became easier on my brain when I studied Riemann’s generalized co-ordinate geometry at Cambridge later on, and it does not distress me that our
evolutionarily
conditioned powers of visualization are inadequate to them. The more recent postulation and subsequent detection of black holes, formed by an old star collapsing into a little sphere of such density that it draws space closed around itself as if to die in utter seclusion, have for me as a spectator been one of the finest intellectual adventures of our age.

The other great monument of early twentieth-century physics, quantum theory, is conceptually much more testing, and those who really understand it claim that those who claim to understand it show by that very claim that they do not. However, I can see that once again a most dangerous little formula hops out of the mathematics of it at a very early stage: the notorious Uncertainty Principle,

h
. To predict the course of an atomic particle, or indeed of any body, one would need accurate information as to its present position and momentum; but the Principle states that the uncertainty of position multiplied by the uncertainty of momentum cannot be reduced below a certain amount, called Planck’s Constant, so that if one of these quantities is known very precisely the other can be measured only imprecisely, and vice versa. Hence the future is inherently unpredictable and causality is replaced by probability – not through shortcomings in our
understandings
or experimental means but as a fundamental feature of the nature of things.

Since Planck’s Constant is extremely small these ineluctable uncertainties only begin to become apparent at the atomic level, which begins about nine steps down the scale of powers of
ten from everyday life. Quantum theory undoes the comfortable
little
picture we used to have of atoms as like solar systems, with their electrons circling a nucleus. Rutherford in the 1900s used to claim that he solved problems in electron scattering by asking where he himself would go were he an electron, but in truth another reality underlies the world of solid, handleable, entities our imaginations grew up in, and at our present level of evolution mathematics is the only language that can capture it in detail. A long way further down the scale of powers of ten, far past the nucleus at step fourteen, the Uncertainty Principle upsets the
simple 
negative ideas we have of what Pascal would have called the Void, the perfect vacuum of empty space. The more accurately the time of a process is specified the less predictable is the energy involved. For the extremely short interval in which two atomic particles are in collision, a wild fluctuation of energy can manifest itself as mass in accordance with Einstein’s little equation, in fact as a pair of ‘virtual’ particles, an electron and its opposite, a positron, which flash in and out of existence and can influence the interactions of more normal particles. Thus the ‘quantum
vacuum
’ is very different from the utter nothingness of the vacuum as conceived by classical physics; it is a perpetual seethe of being, the source of infinite possibility.

Finally, at what is called the Planck Length, which is about a millionth of a billionth of a billionth of a billionth of a
centimetre
and corresponds to the thirty-fifth downward step in my schema, the Uncertainty Principle may demolish the continuity of space itself. At this scale, say some theorists, huge momentary concentrations of energy whip space into a froth of self-occlusions analogous to the black holes of astronomy, the concept of length loses its coherence, and one cannot approach any nearer to the dimensionless points conceived in pure geometry. What form of reality underlies this ‘quantum foam’ is the subject of theories and mathematizations – superstring theory, Penrose’s ‘twistors’ – so recent and advanced, and probably so evanescent, that to
summarize
my slight understanding of them would be mere name-
dropping
. But I delight in the knowledge that human thought is already probing this incomprehensible space riddled with riddles.

Strangely, images of foam abound at the other end of the scale of powers of ten. At twenty-one steps above the human measure we have the galaxies, of which our Milky Way, containing a
hundred 
billion stars, is one; at step twenty-four, clusters of thousands of galaxies; at twenty-five, a sheet of clusters of galaxies called the Great Wall, three hundred million light years across. This last was until recently the largest known structure, but now seems to be just one of many such sheets surrounding and separating regions of the universe in which galaxies are rare, like the films of liquid in a mass of bubbles.

One more step brings us to the limit of all we can ever observe, at a distance of about fifteen billion light years or a
hundred
million billion billion miles – not that there is nothing to observe beyond this limit, which is really one of time set by the fact that light has not had long enough to reach us from any
further
away, since only fifteen billion years have elapsed since the universe was a dot the size of the Planck Length. ‘Is lú na fríde, máthair an oilc,’ less than a speck is the mother of evil, an old Aran man told me. Everything we see or ever can see is born of that speck, for good or evil. But, according to one of the most audacious speculations of contemporary cosmology, we may call on the existence of indefinite numbers of other universes to explain the properties of this one, including its manifest ability to support intelligent life. For, as Hoyle pointed out a long time ago, physics cannot derive and has to take as given the values of
certain
constants (I have mentioned two, the speed of light, and Planck’s Constant), and if these were only slightly different from what they are we would not be here to comment on the fact. A universe with other values of the universal constants might be too small and short-lived, or too vast and dilute, for stars to form; or its stars might not last long enough for nuclear fusion within them to forge the large nuclei of atoms such as carbon necessary for life; or the whole story might go awry and fade out in some other way.
For some, this fine tuning of the universal constants is proof that we were meant to be, that the Universe or its Creator had
written
us or something like us into the plans from the beginning. But there is no need to abandon a thoroughgoing naturalism even at this extremity of the thinkable. A universe that gives rise to stars long-lived enough to form carbon and the other necessaries of life is also going to produce stars that go on to collapse into black holes; and black holes being portions of space that have closed in on themselves and are no longer in contact with the universe they form in, could be the buds of new universes. Suppose that these offspring universes inherit the constants of their progenitor, with slight variations rather as living things do; then universes that fail to thrive and do not produce black holes will not be represented in the next generation, and those that bear plentiful buds will
preponderate
. So, the reason we find ourselves in a universe
hospitable
to life is that the vast majority of universes are so, for such universes themselves are prolific breeders.

This heartshaking vision of the grounds of our possibility in a perhaps eternal and infinite profusion of universes is strangely like that of the foam of being we glimpse at the other end of the length-scale. We are not desolate creatures helplessly adrift between two deathly abysses. The perspectives I have sketched span the perilous sea of our universe from shore to shore. They are two wings of not-quite-inconceivable breadth and power, that bear us up for a time. Not for long enough, but for a time.

BIRDLIFE (AND A PREFACE)

The fiction ‘Two Reminiscences of London 1970’ is included in
Tales
and
Imaginings
1965–98
,
forthcoming from Lilliput.

THE CURVATURE OF THE EARTH

Most of this essay appeared as ‘The Globe’ in
The
Irish
Review,
No. 25, Winter/Spring 1999

2000.

BALLISTICS

Published in
The
Dublin
Review,
No. 1, Winter 2000

1.

A CAREER IN ART

‘Four-colour Theorem’ was described in Peter Joseph and Tim Drever, ‘Outside the Gallery System: two projects for Kenwood’,
Studio
Interna
tional
,
London, June 1969.

The article on ‘Moonfield’ was published in
Adam
International
Review,
ed. Miron Grindea, London, 1969.

‘Field work 3, A Structured Arena’ (the essay on the wavelike floor) was published in
PAGE
14
(Bulletin
of
the
Computer
Arts
Society),
London, February 1971, and republished in
element,
No. 6, Mermaid Turbulence, Dublin, 1999.

The ‘points’ were described in an essay, ‘Geometer’, published in Tim Robinson,
The
View
from
the
Horizon,
Coracle Press, London, 1997.

FIREWALKING

Published in
The
Recorder,
Vol. 12, No. 2, New York, Fall 1999, and
The
Irish
Review,
No. 25, Winter/Spring 1999–2000.

Catherine Nash’s review is in
The
Journal
of
Historical
Geography,
1997, Vol. 23, No. 3.

THE EXTREME EDGE

The story by Adalbert Stifter was first published as ‘Der heilige Abend’ in 1845, and as ‘Bergkristall’ was included in his
Bunte
Steine,
1853. I thank Barbara Scott for translating it for me. The other books mentioned are: Roy Harrod,
Foundations
of
Inductive
Logic,
London 1956, and E.M. Cioran,
La
Tentation
d’Exister,
Paris, 1956.

CONSTELLATION AND QUESTIONMARK

Quotations from Pascal and Leibnitz are translated from Blaise Pascal,
Oeuvres
Complètes,
ed. Jean Mesnard, Desclée de Brower, 1964.

I learned about Dandelin’s proof from Tzu-Pei Chen’s web site , and my Fig. 13 is based on one of the elaborate diagrams on this site.

For the expansion of the universe see Idit Zehavi and Avishai Dekel, ‘Evidence for a positive cosmological constant from flows of galaxies and distant supernovae’,
Nature,
Vol. 401, 252–4 (1999), and related articles in
Scientific
American,
January 1999.

There is a 50-page appendix in English on the four-colour map
theorem
in: George Spencer-Brown,
Laws
of
Form
/
Gesetze
der
Form,
Bohmeier Verlag, 1997. A new English-language edition of
Laws
of
Form
is in preparation. For the alternative proof by consideration of the ‘uncolourables’ see George Spencer-Brown, ‘Uncolorable Trivalent Graphs’,
Cybernetics
and
Systems,
Vol. 29, No. 4, Philadelphia, 1998.

THE ECHOSPHERE

‘Two Wet Days in Roundstone Bog’ (slightly enlarged) appeared in
The
Irish
Review,
No. 24, Autumn 1999.

A HOUSE ON A SMALL CLIFF

Published in
The
Recorder,
Vol. 12, No. 4, Fall 2000.

THE FINENESS OF THINGS

Published in
The
Recorder,
Vol. 12, No. 4, Fall 2000.

The web site for moth pheromones is at http://www.pherolist.slu.se. The speculation on Darwinian evolution of universes is from Lee Smolin,
The
Life
of
the
Cosmos,
Weidenfeld & Nicolson, London, 1997.

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