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The Hidden Hypotheses Behind the Big Bang It is quite unavoidable that many philosophical a priori assumptions lurk behind the debate between supporters of the Big Bang and the anti-BB camp. The same battle has been waged in physics between the determinists and the opposing viewpoint. Therefore, by way of introduction to this symposium, I would like to discuss, albeit briefly, the many'hypotheses', essentially of a metaphysical nature, which are often used without being clearly stated. The first hypothesis is the idea that the Universe has some origin, or origins. Opposing this is the idea that the Universe is eternal, essentially without beginning, no matter how it might change-the old Platonic system, opposed by an Aristote­ lian view! Or Pope Pius XII or Abbe Lemaitre or Friedmann versus Einstein or Hoyle or Segal, etc. The second hypothesis is the need for a'minimum of hypotheses'-the sim­ plicity argument. One is expected to account for all the observations with a mini­ mum number of hypotheses or assumptions. In other words, the idea is to'save the phenomena', and this has been an imperative since the time of Plato and Aristotle. But numerous contradictions have arisen between the hypotheses and the facts. This has led some scientists to introduce additional entities, such as the cosmologi­ cal constant, dark matter, galaxy mergers, complicated geometries, and even a rest­ mass for the photon. Some of the proponents of the latter idea were Einstein, de Broglie, Findlay-Freundlich, and later Vigier and myself.

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title'Predictability, Stability, and Chaos in N-Body Dynamical Systems'. The Institute was the latest in a series held at three-yearly inter­ vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.

The Symposium was held at the Great Wall Sheraton Hotel in Beijing, China in the period August 25-30, 1986. The decision to concentrate on the observational aspects of modern cosmology was taken in part because this conference has come in a period when there have been several international meetings on one aspect of modern cosmology, namely the early universe and its possible relationship to particle physics. While that approach is extremely exciting, it has the disadvantage that its connection with much of observational cosmology is very indirect. Thus there has been little opportunity to discuss critically the wealth of new data that are now becoming available which bear on the structure and evolution of the Universe but not always on its early history. This Symposium was planned to cover all aspects of observational cosmology, with only comparatively minor excursions into theory. Nearly 200 participants attended from 21 countries. A total of 26 invited papers and 73 contributed papers were given. This meant that everyone worked hard and long from 9 A.M. to about 5:30 P.M. for five of the six days of the conference. In addition to oral contributions, space was made available for poster papers and 56 of these were available for study for the duration of the conference.

Modem dynamics is increasingly participating in the solution of problems raised by as­ tronomical observations. This new relationship is being fostered on one side by the im­ provements in the observations, which in recent years contributed several discoveries of new systems, such as the objects in the Kuiper belt, the pulsar and star companions, to speak only of the most striking ones, and, on the other hand, by the progresses in modem dynamics. The progresses in modem dynamics are due to two factors: the dissemination of fast computers, allowing the numerical studies of very complex systems by a large number of scientists, and the improvement in our understanding of the complex behaviour of Hamiltonian systems. KAM and Nekhorochev theories have shed a light on the subtle and surprizing interplays between regular and chaotic motions; numerical experiments and analytical approximations have shown how these peculiarities are indeed present in astronomically important systems and are instrumental in understanding their formation and evolution.

The visible universe is a small perturbation on the material universe. Zwicky and Sinclair Smith in the 1930s gave evidence of invisible mass in the Coma and Virgo Clusters of Galaxies. Better optical data has only served to confound their critics and the X-ray data confirms that the gravitational potentials are many times larger than those predicted on the basis of the observed stars. Dynamical analyses of individual galaxies have found that significant extra mass is needed to explain their rotational velocities. On much larger scales, tens of megaparsecs, there is suggestive evidence that there is even more mass per unit luminosity. What is this non-luminous stuff of which the universe is made'? How much of it is there? Need there be only one kind of stuff? There are three basic possi bili ties:- all of it is ordinary (baryonic) matter, all of it is some other kind of (non-baryonic) matter, or some of it is baryonic and some is non-baryonic.

Scientists in the late twentieth century are not the first to view galaxy formation as a phenomenon worthy of explanation in terms of the known laws of physics. Already in 1754 Kant regarded the problem as essentially solved. In his Univerlal Natural Hutory and Theory 0/ the H eaven$ he wrote;'If in the immesurable space in which all the suns of the Milky Way have formed themselves, we assume a point around which, through some cause or other, the first formation of nature out of chaoo began, there the largest mass and a body of extraordinary attraction will have arisen which has thereby become capable of compelling all the systems in the process of being formed within an enormous sphere around it, to fall towards itself as their centre, and to build up a system around it on the great scale.... Observation puts this conjecture almost beyond doubt.'More than 200 years later, a similar note of confidence was voiced by Zel'dovicb at an IAU symposium held in Tallin in 1911;'Extrapolating... to the next symposium somewhere in the early eighties one can be pretty sure that the question of the formation of galaxies and clusters will be solved in the next few years.'Perhaps few astronomers today would share Kant's near certainty or feel that Zel'dovich's prophecy has been fulfilled, Many, however, will sympathize with the optimistic olltlook of these two statements.

Since Newton's time many have proposed that gravitation arises from the absorption by material bodies of minute particles or waves filling space. Such absorption would cause bodies to be pushed into each other's shadows. The principal early proponent of this idea was Georges-Louis Le Sage. The essays in this book explore the remarkable three hundred year saga of Le Sage's theory, gravitational shielding and the experiments of Q. Majorana, and new and recent Le Sage Models.