Our whole Universe is governed by just six numbers, set at the time of the Big Bang. Alter any one of them at your peril, for stars, planets and humans would then not exist.

by Sir Martin Rees, Astronomer Royal

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.

Six numbers

As the start of the twenty-first century, we have identified six numbers that seem especially significant. Two of them relate to the basic forces; two fix the size and overall 'texture' of our Universe and determine whether it will continue for ever; and two more fix the properties of space itself:

1 The cosmic number 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. A universe within which omega was too high would have collapsed long ago; had omega been too low, no galaxies would have formed. The inflationary theory of the Big Bang says omega should be one; astronomers have yet to measure its exact value.

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 realisation 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.

= 0.007 Another number, epsilon, defines how firmly atomic nuclei bind together and how all the atoms on Earth were made. The value of epsilon 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, and gold and uranium are rare, because of what happens in the stars. If epsilon were 0.006 or 0.008, we could not exist.

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 dis-tinctive 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.

Why the Universe is so large

The tremendous timespans involved in biological 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.

	The galaxy pair NGC 6872 and IC 4970 indicate the vastness of the Universe. Light from the bright foreground star has taken a few centuries to reach us; the light from the galaxies has been travelling for 300 million years. The Universe must be this big - as measured by the cosmic number N - to give intelligent life time to evolve. In addition, the cosmic numbers omega and Q must have just the right values for galaxies to form at all.
	Photo - European Southern Observatory

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 superiority; 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 (some-times 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.

Cosmology comes of age

The physicist Max Born once 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.

D = 3 The first crucial number is the number of spatial dimensions: we live in a three-dimensional Universe. 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.

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.

Some key features of out 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.

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

A few years ago, I already had 90% 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 99%.

"The most incomprehensible thing about the Universe is that it is comprehensible" is one of Albert Einstein's best-known aphorisms. It expresses 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, makes some stars collapse 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.

Q = 1/100,000 The seeds for all cosmic structures - stars, galaxies and clusters of galaxies - were all imprinted in the Big Bang. The fabric - or texture - of our Universe depends on a number that represents the ratio of two fundamental energies. If Q were even smaller, the Universe would be inert and structureless; if Q were much larger, it would be a violent place, dominated by giant black holes.

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 the problems of the cosmos and the micro-world 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^-33 centimetres. This is twenty powers of ten smaller than an atomic nucleus: as big a decrease 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.

Other universes

0.7 Measuring the sixth number, lambda, was the biggest scientific news of 1998, though its precise value is still uncertain. An unsuspected new force - a cosmic 'antigravity' - controls the expansion of our Universe. Fortunately for us, 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.

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 farther 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 specula-tive, 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.

What distinguishes our Universe from all those others may be just six numbers.

Copyright © 1999 Martin Rees. Extracted from JUST SIX NUMBERS published by Weidenfeld & Nicolson at #12.99