Computational cosmologynotes pdf




















Tritton, E. Thomson, B. Kelly, D. Morgan, R. Smith, S. Driver, J. Williamson, Q. Parker, M. Hawkins, P. Williams, A. Introduction and description. Hao, J. Kubo, R. Feldmann, J. Annis, D. Johnston, H. Lin, T. McKay, Intrinsic alignment of cluster galaxies: the redshift evolution.

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Van Waerbeke, M. Brown, et al. Hilbert, J. Hartlap, S. White, P. Schneider, Ray-tracing through the Millennium Simulation: born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing.

Hildebrandt, S. Arnouts, P. Capak, L. Moustakas, C. Wolf, F. Abdalla, R. Assef, M. Banerji, N. Brammer, T. Carliles, D. Coe, T. Dahlen, R. Feldmann, D. Gerdes, B. Gillis, O. Ilbert, R. Kotulla, O. Lahav, I. Li, J. Miralles, N. Purger, S. Schmidt, J. Hirata, U. Seljak, Intrinsic alignment-lensing interference as a contaminant of cosmic shear. D 70 6 , Hirata, R. Ishak, U. Nichol, K. Pimbblet, N. Ross, D. Hoekstra, B. Jain, Weak gravitational lensing and its cosmological applications.

Hoekstra, H. Yee, M. Gladders, Properties of galaxy dark matter halos from weak lensing. Holmberg, A study of physical groups of galaxies. Hopkins, N. Bahcall, P. Hoyle, The origin of the rotations of the galaxies, in Problems of Cosmical Aerodynamics , , p. Hoyle, Galaxies, nuclei and quasars. Hu, Power spectrum tomography with weak lensing.

Hu, G. Wu, G. Song, Q. Yuan, S. Okamura, Orientation of galaxies in the local supercluster: a review. Space Sci. Hubble, Extragalactic nebulae. Huff, G. Graves, Magnificent magnification: exploiting the other half of the lensing signal. Hui, J. Hung, H. Huterer, M. Takada, Calibrating the nonlinear matter power spectrum: requirements for future weak lensing surveys.

White, Nulling tomography with weak gravitational lensing. D 72 4 , Takada, G. Bernstein, B. Jain, Systematic errors in future weak-lensing surveys: requirements and prospects for self-calibration. Joachimi, S. Bridle, Simultaneous measurement of cosmology and intrinsic alignments using joint cosmic shear and galaxy number density correlations. Joachimi, P. Schneider, The removal of shear-ellipticity correlations from the cosmic shear signal via nulling techniques.

Schneider, The removal of shear-ellipticity correlations from the cosmic shear signal. Influence of photometric redshift errors on the nulling technique. Joachimi, R. Mandelbaum, F. Abdalla, S. Joachimi, E. Semboloni, P. Bett, J. Hilbert, H. Schneider, T. Schrabback, Intrinsic galaxy shapes and alignments—I.

Semboloni, S. Hilbert, P. Hartlap, H. Schneider, Intrinsic galaxy shapes and alignments—II. Modelling the intrinsic alignment contamination of weak lensing surveys. Jones, The origin of galaxies: a review of recent theoretical developments and their confrontation with observation.

Kaiser, Weak gravitational lensing of distant galaxies. Kaiser, G. Wilson, G. Luppino, Large-scale cosmic shear measurements. Kang, F. Yang, S. Mo, C. Li, Y. Jing, The alignment between satellites and central galaxies: theory versus observations. Kasun, A. Evrard, Shapes and alignments of galaxy cluster halos. Katz, M. Fardal, R. Cold mode and hot cores. Kiessling, M. Cacciato, B. Joachimi, D. Kitching, A. Leonard, R. Mandelbaum, B. Rassat, Galaxy alignments: theory, modelling and simulations.

Kilbinger, Review article: cosmology with cosmic shear observations. Kim, E. Linder, R. Miquel, N. Mostek, Effects of systematic uncertainties on the supernova determination of cosmological parameters. Kimm, J. Slyz, C. Pichon, S. Kassin, Y. Dubois, The angular momentum of baryons and dark matter halos revisited. King, P. Schneider, Separating cosmic shear from intrinsic galaxy alignments: correlation function tomography.

Kirk, S. Schneider, The impact of intrinsic alignments: cosmological constraints from a joint analysis of cosmic shear and galaxy survey data. Kirk, A. Rassat, O. Host, S. Bridle, The cosmological impact of intrinsic alignment model choice for cosmic shear.

Kirk, M. Brown, H. Joachimi, T. Kitching, R. Mandelbaum, C. Cacciato, A. Choi, A. Kiessling, A. Leonard, A. Rassat, B. Taylor, Path integral marginalization for cosmology: scale-dependent galaxy bias and intrinsic alignments. Taylor, A. Heavens, Systematic effects on dark energy from 3D weak shear. Amara, F. Abdalla, B. Joachimi, A. Refregier, Cosmological systematics beyond nuisance parameters: form-filling functions.

Kitching, S. Balan, S. Bridle, N. Cantale, F. Courbin, T. Eifler, M. Gentile, M. Gill, S. Hirsch, K. Honscheid, T. Kacprzak, D. Kirkby, D. Margala, R. Massey, P. Melchior, G. Nurbaeva, K. Patton, J. Rhodes, B. Rowe, A. Taylor, M. Tewes, M. Viola, D. Witherick, L. Voigt, J. Young, J. Alsing, T. Heymans, H. Hoekstra, A. Jaffe, A. Kiessling, Y. Benjamin, J. Coupon, L. Fu, M. Hudson, M.

Kilbinger, K. Kuijken, B. Rowe, T. Schrabback, E. To browse Academia. Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Computational Linguistics - An introduction. Thennarasu Sakkan. Close mobile search navigation Article navigation.

Volume 27, Issue 2. Previous Article Next Article. Article Navigation. November 02 This Site. Google Scholar. Sandhya Samarasinghe , Sandhya Samarasinghe. Samarasinghe lincoln. Michael Levin Michael Levin. Tufts University, Allen Discovery Center. Author and Article Information. Tran Nguyen Minh-Thai. Sandhya Samarasinghe. Michael Levin. This is, however, only the most apparent aspect of things. The omnipresence of a world ever more "worldly" is only the effect, in the practical order, of a more decisive cause that is theoretical in nature, namely the revolution of Galilean science, its technical progress being only its consequent confirmation.

For the religious soul, the importance of the scientific revolution consists in the fact that it affects this soul's own inwardness. Whereas the scientific revolution, insofar as it ascribes the truth to itself, imposes itself irresistibly and from within on the intelligence that it besieges.

It is a cultural and therefore a "spiritual" revolution to the extent that it makes an appeal to our mind. But whenever it is a question of a believer's mind, it is the vision of the world and the reality implied by his faith that is subverted. What remains then is the option either to renounce his faith, or else--an almost desperate solution-to renounce entirely the cosmology that it entails.

On the whole Christian thought has committed itself to this second way: to keep the faith but a "purified" faith! This 5 The Wisdom of Ancient Cosmology is a desperate solution because these cosmological representations are first scriptural presentations, the very forms by which God speaks to us about Himsel But if we disregard these forms, what remains of our faith?

Scripture informs us that the apostles saw Christ raised from the earth and disappear behind a cloud, while Galilean science objects that space is infinite, that it has neither high nor low, and that this ascension, even supposing it to be possible-which it is not-is meaningless. What remains is then to see in it a symbolic fiction by which the early Christian community attempted to speak its faith in a vanished Jesus Christ: if He is no longer visible, this is because He has "gone back to heaven.

According to Bultmann, what is mythological is a belief in the objective reality of revelation's cosmological presentation: "descent," "resurrection," "ascension," etc. To demythologize is to understand that this cosmological presentation is, in reality, only a symbolic language, in other words, a fiction.

To pass from myth to symbol, this is the hermeneutic that enables a modern believer, living at the same time in two incompatible universes-that of the Bible and of Galilean science-to avoid cultural schizophrenia. But at what price? At the price of making unreal all biblical teachings on which faith relies and with which it is bound up. To reject this cosmological presentation, the witnesses of which the apostles, for example, vouch to have been, is this not to reject with the selfsame stroke the faith attached to it?

What does this parting of faith from its cosmological garment, of kerygma from myth, imply? Basically, would this not separate the Divine Word from its carnal covering and ultimately deny the Incarnation?

How surprising that another way never occurred to Bultmann, a way which, had it been taken into consideration, might have changed many things in the course of the West's religious history.

It is this way that the distinguished mathematician Wolfgang Smith proposes to explore, and into which he now offers us insights. In the present crisis, in which Christian thought is split between an impossible fideism and its confinement to moral problems, Wolfgang Smith's book discloses 'a liberating perspective which, in the name of science itself, restores to faith its entire truth. It would be hard to exaggerate the importance of such a work. What is involved is a fact simple to state: the advent of the theory of relativity and of quantum physics entails the abandonment of the Galilean, model of the universe, a definitive abandonment; or better put, the Galilean' model remains valid as an initial rough estimate which gives a convenient-: although quite inexact--description of the universe.

However simple to, 6 Foreword enunciate, this fact is rife with extremely complex implications which science is still powerless to encompass within a general and unified theory. I will only say that our idea of the cosmos must be completely transformed both in its spatio-temporal structure relativity as well as in regard to the constitution of matter quantum theory , assuming that it is still possible to make any representation of the universe at all.

In any case, today it is nineteenth century materialism that has become a superstition. The rise of relativity and quantum theory, moreover, do not constitute recent events: they occurred at the beginning of the twentieth century.

And so for a hundred years the cosmological and epistemological landscape of our culture has been reshaped profoundly. Philosophers, theologians, and exegetes are, however, far from realizing this; such is Bultmann's situation. The "scientific" vision of the world that he opposes to the mythological vision of faith is that of a science largely obsolete at the time when, in , he expounded his program of demythologization Entmythologisierung.

And though he did occasionally bring up the theory of relativity, it was in passing, and in order to deny that the facts had significantly changed; thus he overtly continued to think withiQ. And that has not altered. Still today the Catholic Church is mocked for condemning Galileo in the name of a retrograde world view, whereas those who do so are themselves prisoners of an obsolete cosmology. One is ridiculed and blamed for belonging to such a Church, and made ashamed of a past judged disgraceful on grounds that have proved invalid.

It is high time to become truly aware of the cosmological revolution that has occurred. To this end I do not think there is a more useful and efficacious work than the one by Wolfgang Smith that I have the pleasure of prefacing. On the most essential points, the most burning questions concerned with biblical cosmology, heliocentrism, the nature of space and matter, the concept of a true causality, etc.

This does not, for all that, involve a new concordism, that is to say that more or less clumsy effort pursued in the nineteenth century and even at the beginning of the twentieth to reconcile the biblical with the scientific worldview. The error of this concordism lies not so much in seeking to rediscover the theses of physics in scriptural teachings a need for unity is natural to reason , but in sharing with official science the conviction that the world is an exclusively material reality, entirely defined by its space- time coordinates.

Basically, when it comes to creation, these theologians were as materialist as Descartes had been in regard to physics. But, to understand this and provide a true interpretation, one requires recourse to the speculative keys offered by traditional cosmology. Wolfgang Smith accomplishes this task in a remarkably precise way, thereby revealing a depth of culture that is able to refer, for example, to the teachings of hermetic philosophy and Germanic theosophy Jacob Boehme, Franz von Baader, etc.

I would add that this concept could also be related to that of internal extemion extensio interna , used in theology especially by Suarez to account for the real presence of Christ's body in the Eucharist: the latter is in fact to be found there with the distinction of its various parts and the relationships that order these parts among themselves, but according to an essential mode and unconnected to the exterior place that circumscribes them in its carnal mode of existence.

It is here, in the rigorous application of traditional keys, that the work of Wolfgang Smith manifests its originality and importance. As I have said, no concordism is involved. But neither is it a question of purely and simply rejecting relativity and quantum theory as having, by definition, no value before faith's transcendent affirmations. This negative attitude was that ofRene Guenon. Certainly, better than any other thinker, Guenon knew how to restore sacred metaphysics and cosmology in their truth, and this is rightly why Wolfgang Smith draws inspiration from his doctrine.

But, with respect to recent physics, Guenon's attitude is somewhat misleading: for him it is only one production among others of a world that he condemns en bloc. Moreover, he does not seem to have any knowledge of quantum theory; as for relativity, he alludes to it but briefly and sees in it only a mathematical nominalism.

Wolfgang Smith treats science differently. Without in any way aspiring to rehabilitate modern science, which quite often is only-as Guenon says- "un savoir ignorant," he yet observes that thls science, by breaking away from the narrow materialism of classical physics, nullifies the objections raised by Galilean mechanics against the data of faith; at the same time, however, he imperiously demands that it be completed and rectified by a metaphysical interpretation based upon traditional doctrine.

This was not the case with Galilean physics which seemed to have succeeded in reducing the world to a material expanse, by rendering physical reality and mathematical rationality identical. To Napoleon's question Laplace replied: "God?

I have no need of this hypothesis! Contrary to what Heidegger maintains, they have proven that science also strives to think. But to do so it is still necessary to wield conceptual instruments.

I will not refer to the many questions broached by Wolfgang Smith, but only mention the admirable analyses developed in Chapter 7, "The Pitfall of Astrophysical Cosmology. Next he establishes that physics, when applied to celestial bodies, having de facto no operational value in that domain, has necessarily an ontological significance, which however is illegitimate. If in fact sidereal bodies, as required by quantum theory, are composed of an almost nonexistent dust of particles, these bodies themselves, as identifiable realities, vanish into space.

For a body un corps is also a body un corps ; a being that is not a being is no longer a being, says Leibniz. Now quantum theory has nothing to say about the existence of this unitary principle needed to account for the reality of a body: it is therefore truly incapable of accounting for the reality of any corporeal being, be it stellar or earthly which is why some physicists have fallen into an idealism insupportable in other respects.

Hence it is absolutely necessary, as Wolfgang Smith reminds us, to have recourse to what traditional philosophy calls a "substantial form," a unitary principle that endows a material body with its own reality. This is no speculative luxury that might be dispensed with, but a rigorously scientific need, since it is the incontestable truth of quantum physics itself that, for want of this substantial form, renders the reality ofbodies forever inexplicable and indeed impossible.

We should be thankful to Professor Wolfgang Smith for having reminded us of these primary truths with the authority of a recognized scientist and the full resources ofhis broad philosophic and religious culture. This ideology has turned science a certain kind of science! Basically, Wolfgang Smith shows us, with simplicity and sometimes with much humor, that Bultmann has chosen the wrong object: it is not religion but the customary interpretation of science that needs to be "demythologized.

France june , Introduction A cording to its title, this book has to do with ancient cosmology. Strictly speaking, however, its primary concern is with traditional cosmology, which is not the same thing. Yet the fact remains that the ancient cosmologies tended to be traditional in varying degrees, which means that the book has to do with ancient cosmology after all.

Nonetheless, it is imperative to distinguish between the two conceptions. To speak of"ancient" doctrine is to speak in historical terms; what renders a doctrine "traditional," on the other hand, is precisely the fact that it is more than historical, more than a mere historical contingency, which is to say that it embodies an element of revelation.

What exactly that means, moreover, is something that only traditional doctrine itself can disclose. Suffice it to say that a doctrine is traditional by virtue of the fact that it partakes somewhat of eternity. It has power, therefore, to inspire the comprehensor, to awaken in us what the poet terms "intimations of immortality.

Paul, it leads from "the things that are made" to the "invisible things of God. On account of what St. Paul terms a "darkening of the heart," the spiritual content of sacred doctrine becomes progressively obscured.

And this appears to be especiallyt:rue in the case of cosmological teachings, the spiritual significance of which has become almost totally forgotten in modern times. This collective process of obscuration, moreover, traces back to the earliest historical periods, and was well under way even while the doctrines in question were still accepted as normative in their external sense.

One knows, however, that "the letter killeth," and that the outer sense of a sacred doctrine cannot for too long survive the demise of its inner dimension. It is perhaps surprising, thus, that ancient cosmology survived in Europe, at least in some of its outer forms, for as long as it did: roughly until the Enlightenment, when it came to be replaced by paradigms of a very different kind. II The Wisdom of Ancient Cosmology One sees, in light of these observations, that one cannot expound or delineate traditional cosmology as one would, say, the facts of botany, or the history of Greece.

Yet there are principles to which all traditional cosmology conforms, and these can be delineated, and can serve from the start as guide-posts along the path of discovery. I propose now to enunciate four such principles, in a kind of ascending order. The first is quite simple: it affirms that traditional cosmology has to do primarily with the qualitative aspects of cosmic reality, the very component, thus, which modern cosmology excludes.

As we shall have occasion to see, this first recognition, simple though it be, has already enormous implications. The second principle relates to the metaphysical notion of verticality and affirms a hierarchic order, in which the corporeal domain, as commonly understood, constitutes but the lowest tier. The transition from traditional to contemporary cosmology entails thus a drastic diminution, an ontological shrinkage of incalculable proportions, which of course pertains, not to the cosmos as such, but to the horizon of our worldview.

As if to compensate for this reduction, contemporary cosmology imputes spatia-temporal magnitudes to the universe at large that stagger the imagination by their sheer quantitative immensity. The fact remains, however, that the spatia- temporal universe in its entirety constitutes but the outer shell, so to speak, of the integral cosmos, as conceived according to traditional cosmology.

The third principle presupposes the preceding two, and affirms that man constitutes a microcosm or "universe in miniature," which in a way recapitulates the order of the integral cosmos itself. This recognition, moreover, might well be singled out as the defining characteristic of the traditional worldview, which can in truth be characterized as anthropomorphic.

I say "in truth," because what stands at issue is an ascription of anthropomorphism which is not merely poetical or imaginary, but factual. Tradition maintains that man and cosmos exemplify, so to speak, the same blueprint, the same master plan.

This means, first of all, that even as man is trichotomous, consisting of corpus, anima and spiritus, so too does the cosmos prove to be tripartite, consisting of what Vedic tradition terms the tribhuvana, the "three worlds. I would like from the start to call attention to the fact that the possibility of human knowing is predicated upon this claim; as Goethe has beautifully put it: if the eye were not kindred to the Sun "wiire das Auge nicht sonnenhaft" , it could not behold its light.

In the final count, man is able to know the cosmos precisely because he is in fact a microcosm. According to the prevailing worldview, man is indeed a stranger in the universe, an accidental and ephemeral product of blind forces. So far from constituting a microcosm, he is a most unlikely anomaly, a precarious molecular formation of astronomical improbability.

Except for the laws of physics and chemistry, which are presumably operative in the cells of his body even as they are in stars and plasmas, he enjoys no kinship whatever with the universe at large, which presents itself as indifferent and ultimately hostile to his human aspirations.

And again, let us note from the start that the new and ostensibly scientific cosmology is in principle incapable of accounting for the fact that man has the capacity to know, limited though his knowledge may be. It turns out as we shall have occasion to see that contemporary science is unable to account for even the most rudimentary act of cognitive sense perception, let alone for the higher modes of sensory and intellective knowing.

The fact is that we can know the cosmos, because, in a profound sense which only authentic tradition can bring to light, the cosmos pre-exists in us.

Only a cosmology, thus, which admits the traditional conception of man as micro,cosm, can account for what may well be termed the miracle of human knowing. The fourth and final principle of traditional cosmology which I would like to point out pertains to its intimate connection with the spiritual ascent of man, as conceived according to the sapiential schools. It affirms that the higher strata of the integral cosmos can be known or entered experientially through the realization of the corresponding states of man himself, in what may indeed be termed an itinerarium mentis in Deum, a "journey into God.

Bonaventure's expressive phrase. The key to knowledge is thus to be found in the Delphic injunction "Know thyself": in the final count, there is no other way, no other means of knowing. We are able, at present, to know the corporeal world, because we have actualized the corresponding state: this is what constitutes, so to speak, our human condition. Occultists and New Age practitioners, it seems, are able in some instances to break into the lower reaches of the intermediary plane, sometimes termed the astral; to ascend beyond that level, on the other hand, is doubtless the prerogative of sages and saints.

The relation between traditional cosmology and spiritual ascent is however twofold: not only are the higher levels of cosmic manifestation to be known through the actualization of corresponding spiritual states, but conversely, a certain preliminary knowledge of the cosmic hierarchy, as depicted, for instance, in iconographic representations, can serve as an aid to the spiritual ascent itself.

From this point of view traditional cosmology becomes an adjunct to religion, a means to the attainment of spiritual realization. Given what we know today about the universe-its origin, its configuration, and its laws-is it logically defensible to maintain the principles and tenets of that traditional cosmology?

To be sure, most people today, be they scientists, philosophers, or theologians, would unhesitatingly answer in the negative. They take it as self-evident that modern science has once and for all disqualified the "primitive conjectures" of pre-modern cosmology. This judgment accords, moreover, with the prevailing evolutionist outlook, which perceives everything as arising "from below," and is therefore disposed to give pride of place to the latest turn of the evolutionary trajectory.

One may wonder, of course, what the next turn might bring, and whether perhaps a still more highly evolved humanity could perceive things differently; but these are questions, in any case, which evolutionists are not prone to ask. Other individuals, comprising a less numerous category, profess high respect for the ancient doctrine, while they implicitly deny its truth. I am thinking especially of those who seem bent upon "psychologizing" every ancient cosmological belief, as if cosmology had to do simply with human fantasies.

This brings us to a third group, which seems to take the ancient doctrines at their word while likewise accepting the outlook of contemporary science, as if there were not the slightest conflict or appearance of incompatibility between these respective claims.

I have in mind, for example, individuals who cheerfully cast horoscopes and interpret these in more or less traditional terms, without realizing that this makes little sense in an Einsteinian universe. Diverse as these respective mentalities may be, they exhibit a common deficiency. What I find conspicuously lacking in each case is any mark of critical acumen, any sign that a searching critique of the prevailing has taken place; yet a critique that penetrates to the very foundations of that worldview is today the sine qua non for a sane approach to cosmology.

Whatever we may think about the past, we live in a present dominated intellectually by the science of our day; and that science needs to be deeply probed and in a way transcended in order to access whatever treasures of wisdom the past may hold. As Theodore Roszak has sagaciously observed: "Science is our religion, because we cannot, most of us, with any 14 Introduction living conviction, see around it. This may be the reason, I surmise, why there are today few if any "intellectual" saints, the likes of St.

Augustine, lets us say, or of St. Thomas Aquinas; it seems to be almost a precondition for sanctity, these days, to have escaped a university education, a fact which augurs ill for the state of theology.

But be that as it may, my point is that "the barrier of scientistic belief" can indeed be breached, which is to say that it is possible, intellectually, to overcome the preconceptions of modernity and postmodernity alike, and thus to rejoin the pre-modern human family.

This does not of course bestow instant illumination; yet what we do gain, most assuredly, by such an intellectual breakthrough, is a distant vision, at least, ofhigh and sacred truths, which in itself is priceless and irreplaceable, and greater by fur than any imagined wisdom which we do not possess.

By the grace of God we do come to perceive truth, though it be "through a glass, darkly. I mplicit in all that I have said is the premise that the principles and tenets of traditional cosmology have not in fact been disqualified by the positive findings of contemporary science. To verify this contention, one needs to engage in the kind of critique alluded to above, and by way of a rigorous analysis, to arrive at a separation of scientific fact from scientistic fiction.

Yet in reality this is only half of what needs to be done; for it is likewise imperative to interpret what science has disclosed, to make sense out of its positive findings, failing which one inevitably fulls back into some kind of scientistic fantasy.

I contend, however, that to arrive at an authentic interpretation of contemporary science one requires the resources of traditional doctrine itself. In an earlier monograph, entitled The QJHzntum Enigma, I have carried out an approach of this kind for physical science as such, with the result that its generic object-the physical universe, properly so called--could be integrated into the traditional ontologies as a sub- corporeal domain.

As might be expected, this throws light on many questions, and explains things which hitherto had seemed incongruous or even paradoxical. As a rule, one finds that the discoveries of physics which strike us as the most bizarre are those that harbor a major metaphysical truth. Such is the case, for instance, with the well-known facts relating to Lorentz invariance-the phenomena, namely, of time dilation and Lorentz 15 The WISdom of Ancient Cosmology contraction-which admit of a metaphysical interpretation, as we shall have occasion to see in Chapter 5 of this book.

Nothing that is true is lost by ascending to a traditional outlook: from a higher point of vantage one sees, not less, but more. The teachings of the traditional schools, so far from being disqualified by the discoveries of contemporary science, are in fact needed to arrive at a proper understanding of science itsel Enough has been said, I presume, to indicate what this book is about.

What I have to offer is not so much a set of answers to specific questions as it is a generic means of coping with what I perceive to be the major intellectual challenge of our time. The book exemplifies a methodical approach based upon traditional teachings, which in the end leads back, Deo volente, to the perennial wisdom of mankind. This is not to suggest that the task of interpreting science becomes a cut-and-dried affair once one has taken one's stand upon traditional ground: such is by no means the case.

The enterprise presents its own challenge and has its own fascination, enhanced by the fact that the possibilities in this kind ofinquiry are virtually endless. It is my hope that the few initial steps which I have taken along this path will encourage others to enter the field and continue these investigations along various lines; the collective need for the fruits of such labors is great.

One might add, however, that having once arrived, by means of this approach, at the recognition of what contemporary science is actually about, one has no further need to conduct inquiries of this nature; one is then prepared intellectually to attend to "the one thing needful," which is the spiritual ascent itself. One question remains: it may seem, from what has been said, that we are caught in a vicious circle. On the one hand, we need to "break through the barrier of scientistic belief" in order to gain access to the perennial wisdom of mankind, and on the other, we require the resources of that wisdom in order to "break through.

T his book, with the exception of Chapter 11, consists of previously published articles, written during the past few years, each under its own inspiration, so to speak. I did not originally intend that these articles should fit together as chapters of a book; but it happens that they do, due to the fact that each constitutes a step, if you will, along the path outlined 16 Introduction above.

These steps need not be conceived as successive, which is to say that the chapters can be read independently. The first two, let it be said, have been written for special occasions. Chapter 1, in particular, constitutes a slightly abridged version of my contribution to the Library of Living Philosophers volume in honor of Seyyed Hossein Nasr; and it is to be noted that Professor Nasr's response to that article in conformity to the format of the LLP series has been added to the present volume in the form of an appendix.

As the reader might expect, the latter constitutes an invaluable commentary shedding light on the central issues.



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