Music and Space - How western composers and musicians have evoked the universe.

 

MUSIC AND SPACE

How western composers and musicians have evoked the universe

A Workshop for the University of the 3rd Age Geelong, 2009

Dr Patrick Hughes

In April 1990, NASA launched the world's first space-based optical telescope - named after American astronomer Edwin Powell Hubble. In late 2008, NASA launched the final maintenance mission in the telescope's 20 year life. So what better time to consider how western composers and musicians have sought to represent 'the universe' or 'the cosmos' or simply 'space'.   The Ancient Greeks (e.g. philosopher Aristotle) believed that the universe consists of a number of transparent, concentric spheres, each rotating at uniform speeds within each other. The outermost sphere is the unchanging heavens, while the intermediary spheres contained the various planets, with the Earth at the centre (See Diagram 1). Greek mathematician and astronomer Pythagoras (582-496 BC) believed that the rotating spheres are related by the whole-number ratios of pure musical intervals, creating a cosmos in constant motion and in perfect musical harmony - a state described as 'musica universalis' (lit. 'universal music' or 'music of the spheres'). Each sphere emits a specific tone depending on its specific orbit, as a guitar string's tone depends on its length. This 'music' is not literally audible, but expresses a mathematical or harmonic idea.   English philosopher Robert Fludd (1574-1637) devised a three octave celestial scale linking sub-planetary worlds to angelic choirs beyond the stars in a great chain of being (See Diagram 2).
Musica universalis from Music of the Spheres by Mike Oldfield (Mercury Records, 2008)	More recently - in 2008 - English composer and multi-instrumentalist Mike Oldfield (of Tubular Bells fame) released an album called Music of the Spheres.   According to the marketing material, 'the title refers to Oldfield's belief that music should aim to represent the spiritual or other-worldly elements of life - something beyond the mundane and everyday' - which isn't, of course, what everyone before him meant by the phrase!
Music of the Spheres from The Earth Sings Mi Fa Mi by The Receiving End of Sirens (Triple Crown Records, 2007)	In the Middle Ages, there was a scientific revolution in western views of the universe. Nicolaus Copernicus (1473-1543), a Polish astronomer and mathematician, posed the first scientifically based model of a heliocentric universe, which became the accepted view of the relationships between the sun and the planets.   However, the 'musica universalis' theory remained popular in medieval Europe. For example, the German mathematician, astronomer and astrologer Johannes Kepler (1571-1630) believed that the Earth's tonal signature oscillates - mi, fa, mi on the scale - as it orbits the sun, in an endless cycle of misery (by which he meant emptiness) and famine (i.e. a desire for things).   In 2007, Boston experimental rock band The Receiving End of Sirens released an album called The Earth Sings Mi Fa Mi (Triple Crown Records). It includes an instrumental track called … 'Music of the Spheres'!
Kepler's work on planetary motion led to Isaac Newton's discoveries concerning dynamics and gravity. Newton's work survived into the late 19th century, when it began to show its limits at sub-atomic scales, prompting the emergence in the early 20th century of Quantum Theory and Relativity. Each offered opportunities to integrate the small world of sub-atomic particles with the big world of the universe. As part of that tumult, Edwin Hubble made two discoveries in the 1920s that changed how humanity thought about its place in the universe. First, our own Milky Way is but one of many galaxies in the universe; second, the universe is expanding - a notion that led to the current 'Big Bang' theory.   So composers and musicians in the Twentieth Century faced perhaps the musical challenge - how to represent the infinity of space in and through music? English composer Gustav Holst's life (1874-1934) spanned the shift from Newtonian to post-Newtonian physics. The Planets is astrological, not astronomical (hence no 'Earth'): each movement illustrates how a planet influences the human psyche.
Neptune, the Mystic by Gustav Holst, from The Planets. The Vienna Philharmonic Orchestra, conductor Herbert Von Karajan (Polygram, 1991).		However, two movements would influence later composers of 'space' music: Neptune, the Mystic; and Jupiter, the bringer of Jollity (Zeus in Greek mythology). Together, they expressed a tension that would dominate 'space' music for much of the rest of the century. Neptune, the Mystic represented infinite space through ethereal strings, a celestial choir … and lots of echo!
Jupiter, the bringer of Jollity by Gustav Holst, from The Planets. The Vienna Philharmonic Orchestra, conductor Herbert Von Karajan (Polygram, 1991).		In the face of the literally awe-some, almost unthinkable idea of infinite space, humanity is insignificant, yet Jupiter, the bringer of Jollity is suffused with triumphalism (later justified as humanity took its first steps into space). It also features a contrasting sentimental (i.e. 'making a direct appeal to the emotions, especially to romantic feelings') theme as if to remind us that people are more than their triumphs. These contrasting ideas and musical tones will recur.
Theme from The Big Country by Jerome Moross. Performed by L'Orchestra Cinematique from Western Film Themes (Metro Music, 2007).		A more recent attempt to represent space musically is the theme tune of the US movie The Big Country (1958. Dir. William Wyler). Its horizon was closer - the wide open spaces of the American mid-west - but in its representation of those wide open spaces we hear again the combination of awe, triumph and sentiment that we heard in Neptune and Jupiter.

 

Wagons Ho!, the theme from Wagon Train by Jerome Moross. From 100 Greatest TV Themes. Artists unknown.	There is one more influence to note. Jerome Moross - composer of the theme from The Big Country - also wrote the theme from the 1960s TV series Wagon Train. Gene Rodenberry presented the first series of Star Trek as Wagon Train in space!
The theme from Star Wars by John Williams. From 100 Greatest TV Themes. Artists unknown. (See below re Close Encounters.)	Having assembled the foundations and background, let's listen to some late twentieth century attempts to represent space musically. All the music is from television series or movies, which may explain why it is almost exclusively orchestral. The theme combines awe, triumph and sentiment, but keeps them quite distinct from each other.
The theme from Superman (1978) by John Williams. The BBC Orchestra, from The Greatest Film Scores.	While the Superman movies aren't about space as such, the theme tune is interesting because even though it moves from triumph to sentiment, the sentimental piece seems reluctant to discard the march-time of the fanfare.
Theme from Star Trek: The Next Generation by Alexander Courage and Jerry Goldsmith. Artists unknown. (GNP Crescendo, 1991)	'Awesome space' precedes a triumphal shout!
Hansen's Message and Humanity Taken by Ron Jones. Artists unknown.	The second series of Next Generation included two episodes called The Best of Both Worlds (I and II). Here are two short pieces from those two episodes, each representing 'awesome space'.
The theme from Star Trek III (1998) by James Horner, Jerry Goldsmith and Leonard Rosenman. Artists unknown.	The composers of the theme from the third Star Trek movie handled sentiment very differently, building one crescendo after another.
Theme from Battlestar Galactica by Stu Phillips. From 100 Greatest TV Themes. Artists unknown.	One of Star Trek's many competitors (some would say copiers!) has been the Battlestar Galactica brand. The theme from the first television series has little time for awe - it jumps straight in with triumphalism!
Death is irrelevant by Ron Jones. Artists unknown. (GNP Crescendo, 1991)	The commercial availability of synthesizers in the early 1970s gave composers and performers of 'space' music a musical tool with a scope that was almost as big as their subject. The synthesizer not only produced sounds of awesome scope, it also offered new voices to critics of industrialism and mechanisation. This next piece by Ron Jones comes from The Best of Both Worlds (I and II) in the second series of Star Trek: The Next Generation.

 

Galaxy Formation. Music composed and performed by David Jacopin. From Nebulas and Galaxies.

Finally, we return to our starting point - the Hubble Space Telescope. Here's a chance to see what a synthesizer can do when combined with pictures from Hubble, courtesy of the European Space Agency:

 

John Williams also wrote the score for Close Encounters of the Third Kind, which - strangely - lacked a theme tune.

A 'leapfrog' strategy for bushfire recovery

 

A 'leapfrog' strategy for bushfire recovery

Patrick Hughes  

 

In January 2020, Australia's bushfires continue to kill, injure and displace people, livestock and wildlife and to destroy buildings and infrastructure. Currently, commonwealth and state governments are, of course, focused on protecting people and property and assisting individuals, families and communities to recover.

 

Affected communities that are being protected and assisted at present will, at some point, need to be rebuilt. Already, some individuals are planning to rebuild their lives and their properties - often by replacing buildings that the fires destroyed.

 

Writing a new future

The fires have damaged or destroyed buildings and infrastructure in affected villages and towns so extensively that they have created a 'blank slate' on which fire-affected communities can write a new future. These communities could re-create their villages and towns as 'demonstration projects', showing Australia and the world what a self-sustaining, low energy and low carbon response to climate change can look like.

 

The new villages and towns would feature cutting edge technologies such as renewable, lightweight materials for home construction and insulation, small local combined heat and power (CHP) generators, automated ventilation, sensor-based lighting and many more.

 

Fire-affected rural communities reclaiming their devastated land could capitalise on its capacity to capture carbon - creating another 'demonstration project'. Economist Ross Garnaut¹ believes that Australia has barely explored the possibility to create an industry out of capturing carbon in soils, woodlands and forests and that Australia could capture up to 1bn tonnes a year - nearly twice our annual emissions.

 

 

Bushfire recovery: a 'leapfrog' strategy

With visionary and imaginative political leadership, fire-affected communities can build new villages and towns that:

·      'leapfrog' the current national impasse around climate change and energy security

·      promote innovation in low-carbon technologies, supporting local research centres by commercialising their ideas

·      expand existing, fledgling markets in 'green' technologies and create new ones

·      upgrade the skills and experience of the existing local labour force as it installs the features and technologies required.

 

When governments grasp such opportunities, the economic benefits can be enormous². For example:

·      In the 1980s, the Danish government poured research funds and economic incentives into wind power; by 2009, Denmark produced over half the world's wind turbines.

·      The German government funded research into solar power and required generous feed-in tariffs for solar power; by 2009, Germany produced over half the world's solar panels.

 

1. Garnaut, R. (2019) Superpower: Australia's low carbon opportunity. La Trobe University Press.

2. McNeil, B. (2009) The Clean Industrial Revolution. Allen & Unwin.

Marcus Chown ' Does gravity come in sizes?' The National Newspaper (Abu Dhabi). 13 March 2009

 

Marcus Chown ' Does gravity come in sizes?' The National Newspaper (Abu Dhabi). 13 March 2009

 

Gravity is the universal force. Not only does it stop us getting above ourselves, it keeps Earth orbiting around the sun, our sun swinging around the centre of the Milky Way, the Milky Way in a merry dance around its neighbours and so on upwards. It is the weakest of nature’s four forces, but whereas the other three – electromagnetism and the strong and weak nuclear forces – unleash their full strength only at the scales of atoms and particles, gravity conserves its power to trump all comers in the cosmos at large. Just take any two things that have mass and, whatever their size and wherever they are, they will feel gravity’s grasp in exactly the same way. Or will they?

 

Justin Khoury, now of the University of Pennsylvania in Philadelphia, and his colleagues Niayesh Afshordi and Ghazal Geshnizjani of the Perimeter Institute for Theoretical Physics in Waterloo, Canada are not so sure. They have listed a series of observations that cannot readily be explained with a one-size-fits-all gravity. None of these effects on its own, they stress, necessarily indicates anything amiss. But intriguingly, all of them melt away if you make just one assumption, albeit a controversial one: that how gravity works depends on the scale on which you look at it.

 

If right, the hunch has truly mind-boggling consequences. According to the theory, this variable gravity would be our first glimpse of spatial dimensions beyond our familiar three – dimensions infinitely large, but which remain forever closed off to us. Dr Khoury acknowledges that it seems wacky. But as long as the observational anomalies are not explained, there is a feeling the idea should not be dismissed out of hand.

 

Gravity is a familiar, yet deeply perplexing force. Its story is bound up with two of the greatest names in physics, Isaac Newton and Albert Einstein. In 1687, Newton published his universal law of gravitation, embodied the motion of the planets, the flight of a cannonball and the dropping of an apple – all in one succinct formula. Yet Newton was hard pressed to explain the nature of a force that seem to be transported instantaneously and with unerring accuracy through empty space. It was only in 1915, with Einstein’s general theory of relativity, that a halfway convincing answer was found. According to general relativity, gravity arises because objects with mass or energy warp space and time around them, causing other objects to fall towards them. Now we can predict gravity’s effects from the smallest scales right up to the scale of the solar system with astounding accuracy.

 

However, general relativity is incompatible with the later quantum theories that describe nature’s other three forces. These theories say that forces are mediated by a constant exchange of particles; accordingly, gravity should be transmitted by a quantum particle known as a graviton. General relativity does not allow for such a possibility, so physicists are left seeking a grander framework that will unite gravity and quantum theory into one “theory of everything”.

 

If you care to look on the very grandest of cosmic scales, there is no shortage of niggling indications that something is not quite right. There’s evidence of dark energy, some kind of invisible “stuff” with repulsive gravity that is the best explanation we have for why the universe’s expansion seems to have begun speeding up in recent aeons. Then there is the mystery of “dark flow”, which has emerged from surveys of thousands upon thousands of distant galaxies. Over middling scales of a few hundred million light years, galaxies look as if they are flowing towards a giant central concentration of mass – one so large that it could not possibly have gathered since the big bang. Finally, then there’s the Lyman-alpha forest. Liberally dabbed across the cosmos are tenuous clouds of hydrogen gas, the building blocks of galaxies. These absorb light, creating a distinctive dip in the spectrum of light penetrating through them known as the Lyman-alpha line. From this forest of spectral lines astronomers can deduce the distribution of hydrogen clouds in space. Like the dark-flowing galaxies, they seem more closely clumped together on middling scales than standard cosmology can explain – again, just as if gravity had once been a stronger force binding them together. Overall, there’s weaker gravity on one scale; stronger gravity on another. Surely one theory cannot explain both? Remarkably, that is just what Dr Khoury and his colleagues are claiming.

 

The context of their work is an outgrowth of string theory – the currently favoured route to a theory of everything – known as brane theory, which views our universe as a four-dimensional island or “brane” adrift in a 10-dimensional ocean of space-time. In particular they focused on a set of these theories known as Dvali-Gabadadze-Porrati models after the three theorists at New York University who suggested them. They would be just the ticket for reproducing the gravitational properties of the universe as we see them. They contain hidden dimensions that might nicely explain the weaker gravity seen at the largest scales and the stronger gravity on intermediate scales. But if brane theories have extra dimensions to the ones we can perceive, why can’t we see them? You and I do not see the extra dimensions because we are made up of ordinary particles of matter that are firmly pinned to the brane, they argue.

 

The Standard Model (of sub-atomic physics): Patrick's notes

 

The Standard Model (of sub-atomic physics)

 

The universe is comprised of twelve ‘fundamental particles’, governed by four ‘fundamental forces’. Our best understanding of how these particles and forces operate is called The Standard Model of particles and forces. It was developed in the 1970s and has explained many experimental results and predicted a wide variety of phenomena. The Standard Model covers only three of the fundamental forces – it doesn’t include gravity. Since most people are more familiar with gravity than with any of the other three forces (and certainly with the strong and weak forces), this might seem a major weakness of the Standard Model. However, gravity is a powerful force only on matter in bulk; at the sub-atomic scale of particle physics, gravity has but a negligible effect. So the Standard Model is still an effective model of the universe at a sub-atomic scale, despite its exclusion of gravity.

 

The twelve ‘fundamental particles’

The twelve fundamental particles are divided into two groups of six – quarks and leptons; and each group of six particles is divided into three pairs or ‘generations’. All stable matter consists of lighter, First Generation particles; heavier, Second and Third Generation particles quickly decay to their next most-stable level.

 

‘GENERATIONS’	QUARKS	LEPTONS
First (Lightest, most stable)	‘Up quark’	‘Electron’ (Electrical charge + mass)
	‘Down quark’	‘Electron-neutrino’ (Electrically neutral, no mass)
Second (Heavier, less stable)	‘Charm quark’	‘Muon’ (Electrical charge + mass)
	‘Strange quark’	‘Muon-neutrino’ (Electrically neutral, no mass)
Third (Also heavier, less stable)	‘Top quark’	‘Tau’ (Electrical charge + mass)
	‘Bottom quark’	‘Tau-neutrino’ (Electrically neutral, no mass)

 

The four ‘fundamental forces’

There are four fundamental forces in the universe: the strong force, the weak force, the electromagnetic force and the gravitational force. The four fundamental forces differ in their strength and range; and each force is carried by its own type of force carrier particle or ‘boson’. Thus, particles of matter exchange energy in discrete/fixed (as opposed to variable) amounts because they exchange bosons with each other.

 

	STRONG FORCE	WEAK FORCE	ELECTROMAGNETIC FORCE	GRAVITATIONAL FORCE
STRENGTH	Strongest	Weaker	Weaker still	Weakest
RANGE	Sub-atomic	Sub-atomic	Infinite	Infinite
ASSOCIATED BOSON	‘Gluon’	‘W and Z’ bosons’	‘Photon’	‘Graviton’ (Yet to be found)

 

A crude chronology of the universe

13.7 billion years ago	The Big Bang
A few billionths of a second later (Around 2,000 billion degrees – 100,000 times hotter than the Sun’s core)	Quarks and electrons emerged. At this stage, they existed freely in a new state of matter – ‘quark-gluon plasma’. (CERN experiments in the late 1990s supported this theory. The Large Hadron Collider’s ‘ALICE’ experiment will re-create these conditions, enabling scientists to study the quark-gluon plasma as it expands and cools, progressively creating the particles that constitute the matter of the universe.))
A few more billionths of a second later	Quarks aggregated into protons and neutrons. They are stuck together by gluons (the carrier particles of the strong force) so tightly that it has proved impossible so far to extract individual quarks or gluons.
Three minutes later	Protons and neutrons aggregated into nuclei
380,000 years later	Electrons were trapped in orbit around nuclei, forming the first atoms. These were mainly helium and hydrogen – still the most abundant elements in the universe.
1.6 million years later	Under gravity, clouds of gas began to form stars and galaxies.
‘Subsequently’	Heavier atoms, such a carbon, oxygen and iron, have been ‘cooked’ continuously in the hearts of stars and distributed throughout the universe each time a star ends as a supernova.

 

What remains?

The Standard Model can’t explain many things, including the existence of ‘dark matter’ and dark energy’, the origin of particle mass and the disappearance of anti-matter.

 

The ‘Dark’ side of the universe

the universe is defined not so much by the ‘things’ that make it up as by the void around them. Observations have shown that the description and chronology above accounts for only 4 per cent of the universe; the remaining 96 per cent consists of ‘dark matter’ (26 per cent) and dark energy’ (70 per cent). Neither emits electromagnetic radiation, so we detect them only through their gravitational effects. We know neither what each is nor what role it played in creating the universe. To answer those questions requires replacing the Standard Model.

 

 

Find the Higgs Boson!

In the 1970s, scientists found very close ties between the weak force and the electromagnetic force, enabling them to describe the two forces within the one theory – the basis of the Standard Model. This theory implies that electricity, magnetism, light and some types of radioactivity are all manifestations of the same force – the ‘electroweak force’. However, while the carriers of this ‘electroweak force’ – the ‘W and Z bosons’ - were discovered in 1983, for the theory of the ‘electroweak force’ to work mathematically, force-carrying particles should have no mass – which experiments have shown they do.

 

Higgs, Brout and Englert (1964?) suggested that immediately after the Big Bang, no particles of any sort had mass; but as the universe began to cool, an invisible force and associated boson were formed – ‘the Higgs field’ – and ‘Higgs boson’. This force prevails throughout the universe and any particles that interact with it are given mass by the Higgs boson. The more that particles interact with the Higgs field, the heavier they become; while particles that don’t interact with it have no mass. Finding the Higgs boson would explain why certain particles – but not all - have mass.

 

The Higgs boson is our current best guess at the origin of particle mass and is a key ingredient of the Standard Model. However, physicists have yet to find the Higgs boson. it is hard to identify, because we do not know its mass, so scientists look for it by searching a range of mass within which it is predicted theoretically to exist. This is what the Large Hadron Collider’s ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) experiments will do. If the LHC fails to find the Higgs boson, physicist will have to pose a new explanation for the origin of particle mass.

 

 

Anti-matter

Matter and anti-matter have the same mass but opposite electrical charge; and for each particle of matter there is a corresponding anti-particle. For instance, the negatively charged electron has a positively charged anti-particle called the positron (found in 1932 occurring naturally in cosmic rays). When a particle and its anti-particle collide, they disappear in a flash, as their mass is transformed into energy.

 

For the past fifty years, scientists have created anti-particles as a matter of routine, but no-one has created anti-particles without creating the corresponding particles. In the same way, the Big Bang must have produced equal quantities of matter and anti-matter, but how, then, has the universe persisted, despite the co-creation of the mutually-annihilating particles and anti-particles? The LHC will investigate by studying the ‘beauty quark’ (‘b quark’).

 

 

String theory

We are used to the existence of three dimensions – height, width, depth – and even four when we add (after Einstein) time. String theory poses the existence of six more dimensions, each curled-up so small as to render it undetectable; and suggests that gravity is the weakest of the four ‘fundamental forces’ (and the graviton has yet to be found) because its effect is shared with these other dimensions. High-energy experiments cold prise-open these hidden dimensions just enough to allow particles to move between the 3-D world and other dimensions. This could be manifest as the sudden disappearance of a particle or the unexpected appearance of one!

 

Underlying String Theory is the idea that fundamental particles are not points or dots, but small loops of vibrating string. Thus, all the apparently diverse particles and forces in the universe are ‘merely’ different modes of oscillation of the same type of string.

 

The complexity of String Theory has so far prevented scientists from deriving testable hypotheses. Not only does String Theory involve the study of the geometry of unseen dimensions, but also the structure of each dimension seems arbitrary and can lead to different outcomes. For example, the extra dimensions can ‘curl-up’ in different ways, according to what shape and size is chosen; and some ‘curled-up’ dimensions are so small that it will be hard to obtain direct evidence that they exist.

 

 

Cosmology reading list

 

COSMOLOGY READING LIST

 

Sky and Space magazine (Australia): www.skyandspace.com.au

 

Argyros, A. J. (2007?) A Blessed Rage for Order. 149 Arg/Brf

 

Harrison, E. (2003) Masks of the Universe: changing ideas on the nature of the cosmos.

Brings together fundamental scientific, philosophical, and religious issues in cosmology, raising thought provoking questions. In every age people have pitied the universes of their ancestors, convinced that they have at last discovered the full truth.

 

Hoyle, F., Burbidge, G. & Narlikar, J. V. (2005) A Different Approach to Cosmology.

 

Lachieze-Rey, M. & Jean-Pierre Luminet, J-P. (2001) Celestial Treasury.

A truly beautiful book revealing the richness of astronomical theories and illustrations in Western civilisation through the ages, exploring their evolution, and comparing ancient and modern.

 

Laughlin, R. B. (2007?) A Different Universe: reinventing physics from the bottom down. Basic Books. ISBN 0465038298

 

Lindley, D. (2007?) Uncertainty: Einstein, Heisenberg, Bohr and the struggle for the soul of science. Doubleday. ISBN 9780385515061

 

Lidsey, J. E. (2002) The Bigger Bang.

Introduces some of the biggest cosmic concepts -- the Big Bang, cosmic inflation, superstrings, parallel universes, and the ultimate fate of the cosmos.

 

Longair, M. (2006) The Cosmic Century.

Reviews the historical development of the key areas of modern astrophysics and links the strands together to show how they have led to the extraordinarily rich panorama of modern astrophysics and cosmology.

 

Pecker, J. C. & J. Narlikar, J. (eds) (2006) Current Issues in Cosmology.

Many of the world's leading players in cosmology look at the strengths and weaknesses of the current big bang model in explaining certain puzzling data. A comprehensive coverage of the expanding field of cosmology, this text will be valuable for graduate students and researchers in cosmology and theoretical astrophysics.

 

Silk, J. (2005) On the Shores of the Unknown.

See how cosmologists study cosmic fossils from the distant past to construct theories of the birth, evolution and future of the Universe. Stars, galaxies and dark matter are described.

 

 

Professor John North

Professor John North, who died on October 31 aged 74, published works covering the whole history of Man's fascination with the universe, from the building of the Neolithic long barrows to the theory of black holes, and he brought to his work not only a clarity of expression but also a mathematician's precision.

 

When he published The Ambassadors' Secret (2002), in which he demonstrated astronomical and religious patterns underlying Hans Holbein's portrait of the French Ambassadors, one reviewer likened him to those who claim that "Elvis is Alive". Yet North's analysis of the picture, while controversial, was also, for many, persuasive – and it was typical of his rigorously scientific approach.

First, he pinpointed the time and date captured in the painting from a cylindrical sundial in the picture as being April 11 1533 – Good Friday – and the time as 4pm, when Christ is supposed to have died. Turning to the distorted skull in the foreground, which can be properly viewed only from a point on the right-hand side, North found that from this point a line could be drawn upwards to the eye of Christ on a tiny crucifix barely visible in the top left corner, passing through key points in the picture including the "27" mark on a quadrant. Both the skull and crucifix lines, he found, were at 27 degrees to the horizontal, a number repeated throughout the painting. Twenty-seven degrees would have been the angle of the sun above London at 4pm on Good Friday in 1533. North also found the distinctive shape of a medieval horoscope frame, its edges defined by key points in the picture. He had discovered a similar pattern in a horoscope he had plotted from one of the Canterbury Tales, which he dated to Good Friday 1400. It later emerged that Holbein had finished the title page illustration for the first English edition of Chaucer's stories only the year before he painted The Ambassadors, possibly deriving inspiration from it.

His doctorate was published as The Measure of the Universe: A History of Modern Cosmology (1965). It was praised as "a virtually complete history of modern mathematical cosmological theories" and was reprinted as a paperback in 1990.

 

North's interest in the paraphernalia of medieval astronomy and astrology – astrolabes, almanacs, clocks, calendars and so forth – resulted in a monumental three-volume study of Richard of Wallingford (1976), a 13th-century abbot of St Albans who was also an astronomer and mathematician. North edited, translated and commented upon all the abbot's surviving works, including the oldest surviving description of a mechanical clock, which he found in the Bodleian Library. In God's Clockmaker: Richard of Wallingford and the Invention of Time (2004), North made the case for the English origins of the clock - one of the great turning points in the history of the last 1,000 years.

 

In the late 1960s North published a series of articles on Chaucer, later summarised in Chaucer's Universe (1988), a 564-page survey in which he showed that the poet employed astronomical techniques and used astrological almanacs for structuring his plots, some of which (The Knight's Tale, for example), have parallels with cosmic events. In the preface to the book North admitted that he risked "being bracketed with those who try to prove that Bacon wrote Shakespeare", but the thoroughness of his scholarship was undeniable. A reviewer in the Times Literary Supplement described the book as "one of the century's monuments of scholarship".

 

In 1977 North accepted the chair in the History of Science and Philosophy at Groningen University in the Netherlands, where he rose to be dean of the faculty from 1990 to 1993. Excavations of a Bronze Age burial mound close to his home alerted him to the cosmology of pre-historic cultures. The result was Stonehenge: Neolithic man and the Cosmos (1996), a thorough survey of Neolithic structures in northern Europe, backed up by copious mathematical and astronomical data, in which he suggested that long barrows were used as horizons to view rising and setting stars, and that the configuration of the stones at Stonehenge was to make possible the observation of the setting of the midwinter sun rather than its midsummer rising, as had previously been assumed. This theory, if correct, would suggest that Neolithic man had developed an understanding of fundamental geometrical concepts that we generally associate with Pre-Socratic Greece.

 

North's other works included Horoscopes and History (1986), The Fontana History of Astronomy and Cosmology (1994), an erudite tour de force accessible to the general reader and the expert alike; and the monumental Cosmos, published earlier this year (2008), a 900-page survey of Man's fascination with the stars from prehistoric times to the present.