Just Six Numbers: The Deep Forces That Shape the Universe

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The genesis of the universe elegantly explained in a simple theory based on just six numbers by one of the world's most renowned astrophysicists
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Editorial Reviews

New Yorker
Rees…has written a brief, readable, and profoundly instructive account of where cosmological knowledge stands at this moment…This is the kind of book that transforms not only how you look at a clear winter sky but also how you think about life itself.
New York Times
[Just Six Numbers] manages to be both a deep and an accessible book, and it answers a lot of the questions produced by natural wonderment… The six numbers that [Rees] uses to describe the one universe we can see are not speculative at all, and they have been made accessible to ordinary intelligence by this marvelous little book.
Economist Review
Just Six Numbers makes for a most unconventional page-turner: as with all the best thrillers, one is left dying to know what will happen next.
Astronomer Rees (Cambridge U.) describes new theories in speculative cosmology in language accessible to the lay reader. The "six numbers" in the title refer to six constant values that describe and define everything from the way atoms are held together to the amount of matter in the universe. Coverage includes the relationship between the cosmos and the microworld, gravity, the periodic table, dark matter, planets, stars, and life in the universe. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Natural History
Rees has sometimes been called the astrophysicist' astrophysicist. Now, with his excellent book, he can be anybody's.
Just Six Numbers manages to be both a deep and an accessible book, and it answers a lot of the questions produced by natural wonderment...Most compelling, Rees shows the deep and powerful connections between ourselves and everything else, the way our existence and the nature of the universe are part of one consistent picture...the six numbers that Rees uses to describe the one universe we can see are not speculative at all, and they have been made accessible to ordinary intelligence by this marvelous little book.
The New York Times
The New Yorker
There is nothing stranger than the universe we inhabit. Rees, Britain's Astronomer Royal, has written a brief, readable, and profoundly instructive account of where cosmological knowledge stands at this moment: how the universe took the shape it did, what structures, now prevail in it, and what it will be like many billions of years from now...This is the kind of book that transforms not only how you look at a clear winter sky but also how you think about life itself.
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Product Details

  • ISBN-13: 9780465036738
  • Publisher: Basic Books
  • Publication date: 5/28/2001
  • Pages: 208
  • Sales rank: 412,841
  • Product dimensions: 5.25 (w) x 7.95 (h) x 0.56 (d)

Meet the Author

Matrin Rees is a leading researcher on cosmic evolution, black holes, and galaxies. He has himself originated many key ideas, and brings a unique perspective to themes discussed in this book. He is currently a Royal Society Research Professor, and Great Britain’s Astronomer Royal. Through based in Cambridge University for most of his career, he travels extensively, and collaborates wit many colleagues in the U.S. and elsewhere. He is an enthusiast for international collaboration in research, and is a member of several foreign academies.
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Read an Excerpt

Chapter One


Man is ... related inextricably to all reality, known and unknowable ... plankton, a shimmering phosphorescence on the sea and the spinning planets and an expanding universe, all bound together by the elastic string of time. It is advisable to look from the tide pool to the stars and then back to the tide pool again.
John Steinbeck, The Log from the Sea of Cortez


Mathematical laws underpin the fabric of our universe — not just atoms, but galaxies, stars and people. The properties of atoms — their sizes and masses, how many different kinds there are, and the forces linking them together — determine the chemistry of our everyday world. The very existence of atoms depends on forces and particles deep inside them. The objects that astronomers study — planets, stars and galaxies — are controlled by the force of gravity. And everything takes place in the arena of an expanding universe, whose properties were imprinted into it at the time of the initial Big Bang.

    Science advances by discerning patterns and regularities in nature, so that more and more phenomena can be subsumed into general categories and laws. Theorists aim to encapsulate the essence of the physical laws in a unified set of equations, and a few numbers. There is still some way to go, but progress is remarkable.

    This book describes six numbers that now seem especially significant. Two of them relate to the basic forces; two fix the size andoverall `texture' of our universe and determine whether it will continue for ever; and two more fix the properties of space itself:

· The cosmos is so vast because there is one crucially important huge number N in nature, equal to 1,000,000, 000,000,000,000,000,000,000,000,000,000. This number measures the strength of the electrical forces that hold atoms together, divided by the force of gravity between them. If N had a few less zeros, only a short-lived miniature universe could exist: no creatures could grow larger than insects, and there would be no time for biological evolution.

· Another number, [Epsilon], whose value is 0.007, defines how firmly atomic nuclei bind together and how all the atoms on Earth were made. Its value controls the power from the Sun and, more sensitively, how stars transmute hydrogen into all the atoms of the periodic table. Carbon and oxygen are common, whereas gold and uranium are rare, because of what happens in the stars. If [Epsilon] were 0.006 or 0.008, we could not exist.

· The cosmic number [Omega] (omega) measures the amount of material in our universe — galaxies, diffuse gas, and `dark matter'. [Omega] tells us the relative importance of gravity and expansion energy in the universe. If this ratio were too high relative to a particular `critical' value, the universe would have collapsed long ago; had it been too low, no galaxies or stars would have formed. The initial expansion speed seems to have been finely tuned.

· Measuring the fourth number, [Lambda] (lambda), was the biggest scientific news of 1998. An unsuspected new force — a cosmic `antigravity' — controls the expansion of our universe, even though it has no discernible effect on scales less than a billion light-years. It is destined to become ever more dominant over gravity and other forces as our universe becomes ever darker and emptier. Fortunately for us (and very surprisingly to theorists), [Lambda] is very small. Otherwise its effect would have stopped galaxies and stars from forming, and cosmic evolution would have been stifled before it could even begin.

· The seeds for all cosmic structures — stars, galaxies and clusters of galaxies — were all imprinted in the Big Bang. The fabric of our universe depends on one number, Q which represents the ratio of two fundamental energies and is about 1/100,000 in value. If Q were even smaller, the universe would be inert and structureless; if Q were much larger, it would be a violent place, in which no stars or solar systems could survive, dominated by vast black holes.

· The sixth crucial number has been known for centuries, although it's now viewed in a new perspective. It is the number of spatial dimensions in our world, D, and equals three. Life couldn't exist if D were two or four. Time is a fourth dimension, but distinctively different from the others in that it has a built-in arrow: we `move' only towards the future. Near black holes, space is so warped that light moves in circles, and time can stand still. Furthermore, close to the time of the Big Bang, and also on microscopic scales, space may reveal its deepest underlying structure of all: the vibrations and harmonies of objects called `superstrings', in a ten-dimensional arena.

Perhaps there are some connections between these numbers. At the moment, however, we cannot predict any one of them from the values of the others. Nor do we know whether some `theory of everything' will eventually yield a formula that interrelates them, or that specifies them uniquely. I have highlighted these six because each plays a crucial and distinctive role in our universe, and together they determine how the universe evolves and what its internal potentialities are; moreover, three of them (those that pertain to the large-scale universe) are only now being measured with any precision.

    These six numbers constitute a `recipe' for a universe. Moreover, the outcome is sensitive to their values: if any one of them were to be `untuned', there would be no stars and no life. Is this tuning just a brute fact, a coincidence? Or is it the providence of a benign Creator? I take the view that it is neither. An infinity of other universes may well exist where the numbers are different. Most would be stillborn or sterile. We could only have emerged (and therefore we naturally now find ourselves) in a universe with the `right' combination. This realization offers a radically new perspective on our universe, on our place in it, and on the nature of physical laws.

    It is astonishing that an expanding universe, whose starting point is so `simple' that it can be specified by just a few numbers, can evolve (if these numbers are suitable `tuned') into our intricately structured cosmos. Let us first set the scene by viewing these structures on all scales, from atoms to galaxies.


Start with a commonplace `snapshot' — a man and woman — taken from a distance of a few metres. Then imagine the same scene from successively more remote viewpoints, each ten times further away than the previous one. The second frame shows the patch of grass on which they are reclining; the third shows that they are in a public park; the fourth reveals some tall buildings; the next shows the whole city; and the next-but-one a segment of the Earth's horizon, viewed from so high up that it is noticeably curved. Two frames further on, we encounter a powerful image that has been familiar since the 1960s: the entire Earth — continents, oceans, and clouds — with its biosphere seeming no more than a delicate glaze and contrasting with the arid features of its Moon.

    Three more leaps show the inner Solar System, with the Earth orbiting the Sun further out than Mercury and Venus; the next shows the entire Solar System. Four frames on (a view from a few light-years away), our Sun looks like a star among its neighbours. After three more frames, we see the billions of similar stars in the flat disc of our Milky Way, stretching for tens of thousands of light-years. Three more leaps reveal the Milky Way as a spiral galaxy, along with Andromeda. From still further, these galaxies seem just two among hundreds of others — outlying members of the Virgo Cluster of galaxies. A further leap shows that the Virgo Cluster is itself just one rather modest cluster. Even if our imaginary telephoto lens had the power of the Hubble Space Telescope, our entire galaxy would, in the final frame, be a barely detectable smudge of light several billion light-years distant.

    The series ends there. Our horizon extends no further, but it has taken twenty-five leaps, each by a factor of ten, to reach the limits of our observable universe starting with the `human' scale of a few metres.

    The other set of frames zooms inward rather than outward. From less than one metre, we see an arm; from a few centimetres — as close as we can look with the unaided eye — a small patch of skin. The next frames take us into the fine textures of human tissue, and then into an individual cell (there are a hundred times more cells in our body than there are stars in our galaxy). And then, at the limits of a powerful microscope, we probe the realm of individual molecules: long, tangled strings of proteins, and the double helix of DNA.

    The next `zoom' reveals individual atoms. Here the fuzziness of quantum effects comes in: there is a limit to the sharpness of the pictures we can get. No real microscope can probe within the atom, where a swarm of electrons surrounds the positively charged nucleus, but substructures one hundred times smaller than atomic nuclei can be probed by studying what happens when other particles, accelerated to speeds approaching that of light, are crashed into them. This is the finest detail that we can directly measure; we suspect, however, that the underlying structures in nature may be `superstrings' or `quantum foam' on scales so tiny that they would require seventeen more zooms to reveal them.

    Our telescopes reach out to a distance that is bigger than a superstring (the smallest substructure postulated to exist within atoms) by a sixty-figure number: there would be sixty frames (of which present measurements cover forty-three) in our `zoom lens' depiction of the natural world. Of these, our ordinary experience spans nine at most — from the smallest things our eyes can see, about a millimetre in size, to the distance logged on an intercontinental flight. This highlights something important and remarkable, which is so obvious that we take it for granted: our universe covers a vast range of scales, and an immense variety of structures, stretching far larger, and far smaller, than the dimensions of everyday sensations.


We are each made up of between [10.sup.28] and [10.sup.29] atoms. This `human scale' is, in a numerical sense, poised midway between the masses of atoms and stars. It would take roughly as many human bodies to make up the mass of the Sun as there are atoms in each of us. But our Sun is just an ordinary star in the galaxy that contains a hundred billion stars altogether. There are at least as many galaxies in our observable universe as there are stars in a galaxy. More than [10.sup.78] atoms lie within range of our telescope.

    Living organisms are configured into layer upon layer of complex structure. Atoms are assembled into complex molecules; these react, via complex pathways in every cell, and indirectly lead to the entire interconnected structure that makes up a tree, an insect or a human. We straddle the cosmos and the microworld — intermediate in size between the Sun, at a billion metres in diameter, and a molecule at a billionth of a metre. It is actually no coincidence that nature attains its maximum complexity on this intermediate scale: anything larger, if it were on a habitable planet, would be vulnerable to breakage or crushing by gravity.

    We are used to the idea that we are moulded by the microworld: we are vulnerable to viruses a millionth of a metre in length, and the minute DNA double-helix molecule encodes our total genetic heritage. And it's just as obvious that we depend on the Sun and its power. But what about the still vaster scales? Even the nearest stars are millions of times further away than the Sun, and the known cosmos extends a billion times further still. Can we understand why there is so much beyond our Solar System? In this book I shall describe several ways in which we are linked to the stars, arguing that we cannot understand our origins without the cosmic context.

    The intimate connections between the `inner space' of the subatomic world and the `outer space' of the cosmos are illustrated by the picture in Figure 1.1 — an ouraborus, described by Encyclopaedia Britannica as the 'emblematic serpent of ancient Egypt and Greece, represented with its tail in its mouth continually devouring itself and being reborn from itself ... [It] expresses the unity of all things, material and spiritual, which never disappear but perpetually change form in an eternal cycle of destruction and re-creation'.

    On the left in the illustration are the atoms and subatomic particles; this is the `quantum world'. On the right are planets, stars and galaxies. This book will highlight some remarkable interconnections between the microscales on the left and the macroworld on the right. Our everyday world is determined by atoms and how they combine together into molecules, minerals and living cells. The way stars shine depends on the nuclei within those atoms. Galaxies may be held together by the gravity of a huge swarm of subnuclear particles. Symbolized `gastronomically' at the top, is the ultimate synthesis that still eludes us — between the cosmos and the quantum.

    Lengths spanning sixty powers of ten are depicted in the ouraborus. Such an enormous range is actually a prerequisite for an `interesting' universe. A universe that didn't involve large numbers could never evolve a complex hierarchy of structures: it would be dull, and certainly not habitable. And there must be long timespans as well. Processes in an atom may take a millionth of a billionth of a second to be completed; within the central nucleus of each atom, events are even faster. The complex processes that transform an embryo into blood, bone and flesh involve a succession of cell divisions, coupled with differentiation, each involving thousands of intricately orchestrated regroupings and replications of molecules; this activity never ceases as long as we eat and breathe. And our life is just one generation in humankind's evolution, an episode that is itself just one stage in the emergence of the totality of life.

    The tremendous timespans involved in evolution offer a new perspective on the question `Why is our universe so big?' The emergence of human life here on Earth has taken 4.5 billion years. Even before our Sun and its planets could form, earlier stars must have transmuted pristine hydrogen into carbon, oxygen and the other atoms of the periodic table. This has taken about ten billion years. The size of the observable universe is, roughly, the distance travelled by light since the Big Bang, and so the present visible universe must be around ten billion light-years across.

    This is a startling conclusion. The very hugeness of our universe, which seems at first to signify how unimportant we are in the cosmic scheme, is actually entailed by our existence! This is not to say that there couldn't have been a smaller universe, only that we could not have existed in it. The expanse of cosmic space is not an extravagant superfluity; it's a consequence of the prolonged chain of events, extending back before our Solar System formed, that preceded our arrival on the scene.

    This may seem a regression to an ancient `anthropocentric' perspective — something that was shattered by Copernicus's revelation that the Earth moves around the Sun rather than vice versa. But we shouldn't take Copernican modesty (sometimes called the `principle of mediocrity') too far. Creatures like us require special conditions to have evolved, so our perspective is bound to be in some sense atypical. The vastness of our universe shouldn't surprise us, even though we may still seek a deeper explanation for its distinctive features.


The physicist Max Born claimed that theories are never abandoned until their proponents are all dead — that science advances `funeral by funeral'. But that's too cynical. Several long-running cosmological debates have now been settled; some earlier issues are no longer controversial. Many of us have often changed our minds — I certainly have. Indeed, this book presents a story that I would once myself have thought surprising. The cosmic perspective I'll describe is widely shared, even though many would not go the whole way with my interpretation.

    Cosmological ideas are no longer any more fragile and evanescent than our theories about the history of our own Earth. Geologists infer that the continents are drifting over the globe, about as fast as your fingernails grow, and that Europe and North America were joined together 200 million years ago. We believe them, even though such vast spans of time are hard to grasp. We also believe, at least in outline, the story of how our biosphere evolved and how we humans emerged. But some key features of our cosmic environment are now underpinned by equally firm data. The empirical support for a Big Bang ten to fifteen billion years ago is as compelling as the evidence that geologists offer on our Earth's history. This is an astonishing turnaround: our ancestors could weave theories almost unencumbered by facts, and until quite recently cosmology seemed little more than speculative mathematics.

    A few years ago, I already had ninety per cent confidence that there was indeed a Big Bang — that everything in our observable universe started as a compressed fireball, far hotter than the centre of the Sun. The case now is far stronger: dramatic advances in observations and experiments have brought the broad cosmic picture into sharp focus during the 1990s, and I would now raise my degree of certainty to ninety-nine per cent.

    `The most incomprehensible thing about the universe is that it is comprehensible' is one of Einstein's best-known aphorisms, expressing his amazement that the laws of physics, which our minds are somehow attuned to understand, apply not just here on Earth but also in the remotest galaxy. Newton taught us that the same force that makes apples fall holds the Moon and planets in their courses. We now know that this same force binds the galaxies, pulls some stars into black holes, and may eventually cause the Andromeda galaxy to collapse on top of us. Atoms in the most distant galaxies are identical to those we can study in our laboratories. All parts of the universe seem to be evolving in a similar way, as though they shared a common origin. Without this uniformity, cosmology would have got nowhere.

    Recent advances bring into focus new mysteries about the origin of our universe, the laws governing it, and even its eventual fate. These pertain to the first tiny fraction of a second after the Big Bang, when conditions were so extreme that the relevant physics isn't understood — where we wonder about the nature of time, the number of dimensions, and the origin of matter. In this initial instant, everything was squeezed to such immense densities that (as symbolized in the ouraborus) the problems of the cosmos and the microworld overlap.

    Space can't be indefinitely divided. The details are still mysterious, but most physicists suspect that there is some kind of granularity on a scale of [10.sup.-33] centimetres. This is twenty powers often smaller than an atomic nucleus: as big a decrease — as many frames in our `zoom lens' depiction — as the increase in scale from an atomic nucleus to a major city. We then encounter a barrier: even if there were still tinier structures, they would transcend our concepts of space and time.

    What about the largest scales? Are there domains whose light has not yet had time to reach us in the ten billion years or so since the Big Bang? We plainly have no direct evidence. However, there are no theoretical bounds on the extent of our universe (in space, and in future time), and on what may come into view in the remote future — indeed, it may stretch not just millions of times further than our currently observable domain, but millions of powers of ten further. And even that isn't all. Our universe, extending immensely far beyond our present horizon, may itself be just one member of a possibly infinite ensemble. This `multiverse' concept, though speculative, is a natural extension of current cosmological theories, which gain credence because they account for things that we do observe. The physical laws and geometry could be different in other universes, and this offers a new perspective on the seemingly special values that the six numbers take in ours.

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Table of Contents

List of Illustrations ix
Preface xi
Acknowledgements xiii
1 The cosmos and the microworld 1
2 Our cosmic habitat I: planets, stars and life 14
3 The large number N: gravity in the cosmos 27
4 Stars, the periodic table, and [varepsilon] 45
5 Our cosmic habitat II: beyond our galaxy 58
6 The fine-tuned expansion: dark matter and [Omega] 80
7 The number [lambda]: is cosmic expansion slowing or speeding? 102
8 Primordial 'ripples': the number Q 115
9 Our cosmic habitat III: what lies beyond our horizon? 130
10 Three dimensions (and more) 149
11 Coincidence, providence - or multiverse? 164
Notes 180
Index 186
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  • Anonymous

    Posted February 18, 2003

    Understanding the Universe without all the Math

    True, the title of this book implies mathematical implications. Nonetheless, let me assure you that Sir Martin is a master at translating the mathematically complicated into the easily understandable for those of us who do not possess PhD's in math or astrophysics. If you're just a regular person who's interested in Cosmology, Astronomy, Black Holes, Space Time Theory, etc., this book is for you. Sir Martin may be an Astronomer Royal at Cambridge University in England, but he writes in a very straightforward, easily understandable style. Read this book!

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted May 23, 2001

    Excellent Speculations About the Implications of Cosmology

    Popular science books are often so simplified that little is gained by reading them. Add equations, and some people will ignore the book. Become detailed in mathematics, and more people will be lost. Professor Rees has done a remarkable service in this outstanding book by taking mathematical ratios and exploring their implications in nonmathematical ways. The result builds a totally new metaphor for considering the structure of the universe . . . that of a stable system. He then takes that metaphor and uses it to build an understanding of the important unanswered questions about cosmology and how answers may be derived through a combination of experimenation, observation, and systems analysis. As a result, the nonscientist is brought into the 'thinking' part of these scientific areas without needing to have much scientific background. I was attracted to the book by the concept of how six numbers could explain a great deal about the universe. The development of that theme turned out to be a pleasant surprise. The six numbers are: nu (a ratio of the strength of electrical forces that hold atoms together compared to the force of gravity which is 10 to the 37th power) epsilon (how firmly the atomic nuclei bind together which is 0.004) omega (amount of material in the universe) lambda (force of cosmic 'antigravity' discovered in 1998, which is a very small number) Q (ratio of two fundamental energies, which is 1/100,000) delta (number of spatial dimensions in our universe) Doesn't look overwhelming, does it? Well, that highlights the book's strength, which is to explain the importance of these numbers. Basically, Professor Rees describes the background behind how the numbers were developed, then explores the implications of the number (especially by looking at what happens if the number was much larger or smaller), and then ties the number to implications for other cosmological questions and puzzles. Building from one to the next, he describes the current state of cosmological thinking through an architecture of these six numbers. To this summary of the known science, he adds his own conjectures by way of potential hypotheses for future testing. We are at an interesting time for cosmological study. Because our ability to peer into space is improving rapidly due to advances in space and earth telescopes, more kinds of observations can be conducted to test basic theories about the nature of the forces in the universe. We should expect rapid progress in knowledge, as a result. Stephen Hawking has placed a twenty dollar bet that the elusive 'unified field theory' that frustrated Einstein will appear within twenty years (but you should also know that he just paid off a loss on the same bet). A pathway that follows along understanding superstrings of 10 dimensional matter seems promising in this regard for now. I found the writing to be very appealing in this book. Professor Rees is gifted in using examples to make the incomprehensible more meaningful. He is also ruthless in excising any detail that you do not need to know to comprehend the points he is developing. So you get a lean, compact argument. He writes clearly, which simplifies the reader's task while increasing the reader's pleasure. The text is benefited by several interesting illustrations, as well. After you have finished reading this informative and stimulating book, ask yourself what the implications of a stable system are. Does it mean that some greater hand has been involved? Does it have no further implications, whatsoever? Does it mean that even greater systems should be assumed? How does it square with the notion of entropy (order becoming disordered)? If you are like me, new questions and perspectives will occur to you after reading this book that will greatly increase your interest in and appreciation of cosmology and physics. Look backward and outward to see the future more clearly, and then ask, 'What is the essence?'

    2 out of 2 people found this review helpful.

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  • Posted August 1, 2009

    more from this reviewer

    I Also Recommend:

    Compelling Work

    Originally published in Great Britain in 1999, I bought it in 2007 thinking I was buying a cutting edge book. I was not. However, I was still happy with my purchase as the general ground-rules of physics were still intact. Certainly there are new discoveries such as the search for dark energy that would add to the book's six numbers, but overall it is a decent book that most science buffs will enjoy.

    As a spiritual person I have been on a quest in recent years searching for links between science and a Creator. That is, an intelligent creator. Part of this search has led to the finely-tuned mathematics of physics and the creation itself. Only the brain dead could not be awed by the way the `numbers' and `nature' seem to dovetail in every aspect.

    This book did not answer my questions but it did contribute to the stew and for that I am thankful and pleased.

    I also enjoyed - The Language of God: A Scientist Presents Evidence for Belief, Reinventing the Sacred: A New View of Science, Reason, and Religion, The Science of God: The Convergence of Scientific and Biblical Wisdom, The Mind of God: The Scientific Basis for a Rational World, Beginnings: The Story of Origins-of Mankind, Life, the Earth, the Universe and The Goldilocks Engima: Why Is the Universe Just Right for Life?(although I gave this book only one star for being republished under a new name thereby misleading people to buy the same book twice)

    I took away one star from Just Six Numbers only because of it's birthdate. I hope you find this review (opinion) helpful.

    Michael L. Gooch, SPHR

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted November 9, 2009

    No text was provided for this review.

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