The Anthropic Cosmological Principle

From �The Cosmlogical Principles�

Chapter 6

By Konrad Rudnicki

6.01. Ecological correction to the Copernican Principle

The Anthropic Principle (not Anthropic Cosmological Principle yet) emerged, in fact, in 1973 in connection with the solemn celebration of 500th anniversary of Copernicus's birth. The first publications about it appeared only one year later. Some ideas, very similar to this principle, can be traced back even to the ancient philosophers. If one accepts that any idea of our Universe having some special properties necessary for the existence of human beings is a precursor of the Anthropic Principle, then one can find some elements of it in every religion which states that the Universe or part of it was created for people. Thus, the Anthropic Principle could be regarded as very old indeed, since such statements are involved in many religions. Therefore, according to Oddone Longo (1989), we have to be very careful in comparing the contemporary Anthropic Principle to any old religious or philosophical views. There are many different versions of the Anthropic Principle. They differ not only in formulation but also in content. Thus it is truly difficult to determine when and where the idea of the principle in its contemporary sense first emerged. Probably a group of American, English, French, and German Christian philosophers and scholars active in the 17th century, called "natural theologians", should be regarded as forerunners of this trend. They noticed, for example, the particular property of water, the density of which increases with rising temperature near its freezing point, and they showed that this is of great importance for living organisms. Again, they pointed out the special chemical properties of carbon and a number of other particular facts concerning the human environment which are exploited even today by adherents of the Anthropic Principle. However, statements of the kind can be found much earlier, too. Barrow and Tipler (1987), in their fundamental book on this principle, date its first scholarly antecedents to as early as 500 B.C.

As the first contemporary and fully purposeful publications about this idea, the papers of Whitrow (1955), Idlis (1958) and Dicke (1961) are usually cited. Dicke stated that in many respects human placement within the Universe (in the sense of location in time and space, mean density of matter, degree of isotropy, etc.) is a favorable one and cannot be considered as incidental. Nevertheless, the very idea of an anthropic principle gained popularity only when two scientists preparing independently of each other, on the occasion of celebrating the Great Anniversary of Copernicus, presented their contributions with some modification or supplementation to the Copernican Cosmological Principle.

Igor Karachentsev (1974, 1975) accepted the validity of the Copernican Principle but stated that 'the confrontation of the observational data with the Copernican Principle needs an ecological correction'. This ecological correction consists in the statement that, in fact, the a priori probability of our actual location in the Universe is very, very low. I would like to interpret Karachentsev�s mathematical considerations in a following way. The most probable a priori location of an observer in the Universe would be somewhere in a galaxy cluster structure (today one could say - within some Voronoy foam bubble, or in a more general way - within some intergalactic void). However, we are not located between galaxies. We live within a small, loose, local group of galaxies, and this makes it possible for us to live in a spiral galaxy (the large, compact clusters consist of ellipsoidal galaxies). Only because we are in a spiral galaxy (there are many more elliptical than spiral galaxies in the Universe) our star, the Sun, can belong to a disk subsystem of stars (ellipsoidal galaxies have no disk). Only because we do belong to a disk subsystem (most stars in the Galaxy belong to spherical subsystems) can we have at our disposal so much carbon and water (the presence of heavy elements in a spherical subsystem of stars is very low). Furthermore, we can avoid close encounters with other stars which would be quite tragic events for us. Only because our Sun is a single star (most disk stars are double or multiple systems) can the planetary orbits around it be roughly circular and stable, and thus, the thermic condition can stay more or less the same throughout long epochs.

Only because our Earth revolves around the Sun not too far from and not too close to it (most planetary orbits are located too far or too close) can we have water in a liquid state, which is indispensable for life. Only because our Planet has an relatively massive satellite - our Moon - which causes tides, did life on Earth have the opportunity to go ashore from the sea where it originated; and, according to Karachentsev, this is the condition necessary not only for life but also for civilization to arise here.

To summarize: only this very particular location of our Earth allows for the existence of man, a being which can observe the Universe and explore it. In average, the Universe may look a certain way, but we see it from a very particular place. From our Earth we can see our Moon, planets, the shining Sun, the Milky Way.... In an average place in the Universe, such objects would not be visible at all; in such an average place, we ourselves could not have existed. The location of a conscious observer of the Universe is, necessarily, a rather special one, due to this 'ecological correction' to the Copernican Principle. It was Copernicus who first said: we can observe planetary loops because we ourselves are on a planet. Can he also be counted as one of forerunners of the Anthropic Principle?

Thus the notion of consciousness, which before was consciously avoided in any astronomical, physical or other investigation in the realm of the strict sciences, entered cosmology. It could be said that the Copernican Principle removed man from cosmological considerations. The ecological correction brought man as a conscious being back into the focus of matter.

6.02. Relativistic observer and actual observer

At the same time, Brandon Carter (1974) arrived at conc1usions that our location within space-time is a very particular one; also, there are particular laws of nature governing us. He invoked for the first time the very name of the Anthropic Principle, distinguishing two versions of it: the Weak Anthropic Principle and the Strong Anthropic Principle.

It is not only because of this preferred location in space but also because of particular properties of our cosmic environment that something like human beings can subsist. In order to produce a being not necessarily human, but conscious, striving towards knowledge, and having a physical body (for the angelic beings are not subject to natural scientific investigations), some very special conditions must be fulfilled. In the course of time, more and more of these conditions were found.

Einstein's General Relativity, and thus relativistic cosmology, often makes use of the term 'observer�. This is an imaginary being capable of perceiving certain domains of the Universe. These 'observers' not only play an important role in many relativistic, �mental experiments�, leading to a better understanding of the investigated phenomena, but they even appear as legitimate elements of the theory. When we are expressing the Generalized Copernican Cosmological Principle that the Universe looks from every point thus or so, we have in mind an abstract observer located in an arbitrary point of cosmic space (e.g. on a star or on an intergalactic dust partic1e). G. Whitrow (1955) said that this Einsteinian approach misses the point, that the "great" Universe is an abode of many living organisms, and only as such can it be understood in the right way. The anthropic principle brought to our attention that in cosmology an important role is assigned to the real observers, i.e. physical, conscious beings, striving for knowledge.

6.03. Conditions for the existence of actual observers

If such a real observer exists, he is necessarily endowed with a physical body of a rather complicated structure (something similar to human senses, something resembling the human brain). This can be realized, to the best of our knowledge, only in the realm of chemical compounds of carbon. But carbon as a chemical element can have its very special properties only within a very limited interval of physical constants. Any small variation in Planck's constant or in the electric charge of the electron would result in a radical change of the properties of carbon and prec1ude the life of beings complicated enough to be real observers. Likewise, if the gravitational constant had been only slightly different, stars (according to the Universe models with expansion) either would have been unable to produce carbon at all or would have produced but not ejected it into cosmic space; then, carbon could not have constituted the bodies of living beings. Besides carbon, another substance necessary for life is water. Water can have its beneficial properties only within the existing set of values of physical constants. In the course of time, it became c1ear that all physical laws, all physical constants, all initial conditions of the Universe, as well as its age (cf. e.g. Carr 1982) can be deduced from the assumption that "real observers" (i.e. physical, conscious beings striving for knowledge) do exist in the Universe.

Hawking (1988) provides the following simple formulation: The Anthropic Principle: We see the universe the way it is because if it were different, we would not be here to observe it. John Maddox (1984) formulates this as a paradox: we can derive the values of physical constants from the fact that we know these values. It should be noticed that Carter (1984), who was first to call this complex of facts and problems the Anthropic Principle, confessed later that this very name brought some wrong associations. If he could change the name, he would have called it the 'cognition principle' or the 'self-selection principle'.

6.04. The Anthropic Principle and the arrow of time

If an observer of the Universe is to be humanlike, he has to have a sense of time. His psychological arrow of time must be there, clearly dividing the past from the future. If this observer is a physical being (contemporary cosmologists are not fond of dealing with ange1s), his arrow of time has to be based on some physical time arrow, first and foremost on the thermodynamic one. The discussion whether the increase of entropy, and thus the existence of an arrow of time, is a general property of the physical world, initiated by scientists like Ernest Dermal (1896) and Ludwig Eduard Boltzmann (1897), has not been finished to this day. In the light of the Anthropic Principle, the problem cannot be solved in either an observational or experimental way. We, with our psychology based on time consciousness, can exist only in those regions of the Universe where there is an arrow of time. Thus, everything we perceive around us has a definite direction in time. The substratum can be conceived as ideally homogeneous in respect to space and time but 'deviations from this ideal from symmetry of substrate continuum... or from the symmetry with regard to time direction... make it possible to introduce the observer in a natural way' (Zabierowski 1988a).

6.05. Must every actual observer be humanlike?

One can have objections as to whether the bodily structure of every real observer necessarily requires the same conditions as earthly man. Of course, no physical, intelligent being could live in a world where a universal levitation instead of universal gravitation were the basic physical reality. In such a Universe, all particles would tend to get dispersed, and a body of a being could not have been formed. However, we can conceive a physical being based on another intelligence principle, and then the limits of allowed variation of physical constants might be substantially larger than those usually provided by the adherents of the Anthropic Principle. For one, there is a widespread opinion that a hive (understood as a family of bees not the place where they live) possesses much greater intelligence than the sum of the combined intelligences of the individual bees. One can imagine an intelligent, conscious being striving for knowledge which exists not as one body but as a swarm of small, primitive particles of some sort of dust. Each particle alone would have too primitive a structure to be intelligent by itself, but the swarm as a whole could have a high combined intelligence. Much simpler conditions would have to be fulfilled to sustain the existence of such particles than the existence of one body possessing this required degree of intelligence and consciousness.

Another objection may result from the fact that nobody, up to now, has performed a profound analysis of possible properties of chemical elements which could be formed by various values of physical constants. It is true that by changing any of the physical constants in any way, carbon and hydrogen would lose their properties which are necessary for sustaining life. But, would some other elements then acquire favorable properties? The adherents of the Anthropic Principle usually maintain that, even if there could be life based on other chemical elements and other physical phenomena, it would not have been capable of evolution, that is, it could not have risen above the most primitive level, even if it could have originated in such conditions at all. The opinion that, besides carbon life, there could also be silicon life undergoing evolution, is usually disproved by indicating that carbon dioxide, the gas which makes possible the metabolic processes in plants and animals, is of essential importance for carbon life. Compounds of silicon could be, in principle, useful for living beings, but silicon dioxide is just a solid mineral, in no way suitable for any respiration process. That is true, but nobody can say if the silicon dioxide or another silicon compound would not have been suitable for a metabolism with other values of physical constants.

The objections can go even further. One can ask whether life and intelligence must be based on chemical phenomena at all, for which (according to up-to-date theories) the underlying forces are electromagnetic. We could conceive of gravitational life or life based on nuclear forces. It is usually contended that these interactions are either too "lazy" (gravitation) or too simple (nuclear forces: a nucleus of an atom cannot contain more than 200 elementary particles). Paul Davies (1981) comes to the conclusion that there cannot possibly be gravitational or nuclear life. But do we really know everything about gravitation? Besides, can one be sure that all the existing physical interactions are already known? Michael Friedjung (1987) considers the conditions of life usually alleged by the adherents of the Anthropic Principle to be just not true.

Those who raise these kinds of objections say that, in fact, the Anthropic Principle states nothing more than: 'Man, as he is, can exist only in the Universe as it is', which implies that in other existing or possible universes there can or could exist some other kind of "men." It may be said here that all the physical laws and other properties of the Universe can be deduced not only from the existence of men, but also from the existence of anything that is there as well. A profound analysis and discussion of a grain of sand must lead to the conclusion that such grains of sand can exist only in such a Universe as it is. This kind of opinion can be formulated crassly by stating that the Anthropic Principle is but a tautological statement: 'The Universe with humanity is such as it is'.

However, until either "non electromagnetic" (non chemical) life or a definite set of physical laws or physical constants completely different from those at work in our Universe but still supporting the existence of physical, conscious, intelligent beings is described in detail, the Anthropic Principle has to be accepted, at least as a stimulating suggestion.

6.06. The Principle of Mach as a cosmological principle

The proposition that the Universe, or any arbitrary fragment of it (e.g. humanity), is such as it is, is not as trivial as it looks at first glance. If it only could be true that one fragment can reveal the structure of all the remaining parts! In this case, if the properties of the All can be deduced from any part, it would be the same whether one is concerned with the existence of a scientist or that of a grain of sand. As we stated before (cf. 4.13), Einstein set about creating a theory which should fulfill the Principle of Mach (i.e. a theory which would admit a possibility of reconstructing the structure of all being out of just one of its fragments). Neither Special nor General Relativity does fulfill the Principle of Mach, but this is no proof that Mach's principle as such cannot still be valid.

The aspiration of understanding the total structure of the Universe from one fragment of it involves the conviction that Mach's Principle is valid. If it is, then the Anthropic Principle in its strong version would be just one of many ways of putting the principle to practical use. The Anthropic Principle can be considered as a particular variant of the much broader Principle of Mach (cf. Ellis 1987b). Why then is the Principle of Mach hardly ever called a cosmological principle? Is this only because Einstein eventually failed in his attempts?

When we attempt to construct an adequate model of the Universe based on the phenomena as perceived in its observable region, which is but one fragment of the totality, no matter what physical theories we do apply and what philosophical views we adopt, we are making use, consciously or not, of Mach's Principle. We are inwardly convinced of this principle; we believe in it.

6.07. Weak and strong versions of the Anthropic Principle

For the sake of further discussion, let us formulate the main versions of the Anthropic Principle so that they are representative of its subsidiary formulations.

The Weak Anthropic Principle: The physical properties of the observable part of the Universe have to be taken as a logical conclusion from the premise that the human being observes it. Carter (1984) proposes a simpler definition: Our existence implies restrictions for our location in the Universe. By location we are to understand a location in space-time. Not every cosmic epoch allows our existence. The words here are much more modest; they convey roughly the same sense, but they need more explanation.

By skipping the words "of the observable part" and changing the "human being" to "real observers" in the former definition, one obtains the Strong Anthropic Principle: The physical properties of the Universe have to be taken as a logical conclusion from the premise that real observers exist in some parts of the Universe's space-time. This can be formulated also: Our existence implies restrictions for properties of the Universe.

Carter admits that he cannot defend the Strong Anthropic Principle with the same conviction as the weak one. John D. Barrow and Frank J. Tippler (1986) consider the Weak Anthropic Principle...a culmination of the Copernican Principle (...) that a man can observe only from the point where a man can stand because the former [the Copernican Principle] shows how to separate the features of the Universe whose appearance depends on anthropocentric selection, from those features which are genuinely determined by the action of physical laws (...) The Copernican Revolution was initiated by the application of the Weak Anthropic Principle (...) We observe the retrograde motion (of planets) because we are on a planet.

Thus Barrow and Tipler gave a positive answer to the problem formulated first by Karachentsev. Copernicus should be considered as one of the forerunners of anthropic kind of thinking. But, according to them, this concerns only the Weak Anthropic Principle.

6.08. Purposeful Creation

The Anthropic Principle presents a logical implication only. Various philosophical, and even more diversified cosmological, astronomical, and physical interpretations may be drawn from it. These can be divided into three classes.

Some religiously minded people conclude that here is the proof that the Universe was created in order to make human existence possible. Out of an infinite number of possibilities, the Supreme Creator took one which is conducive to developing life, intelligence, consciousness, and culture. He "had in mind" future humanity when creating the laws of logic and space-time and establishing the initial conditions for the Universe. The logical implication involved in the anthropic principle is considered here as a causal implication. This is the simplest interpretation of the principle, but it is too simple to win wide acceptance. The difference between these two kinds of implications (logical and causal) is assumed here on no basis other than religious conviction, very important, indeed, as such, but by no means equivalent to scientific convictions. In fact, if somebody believes in the teleological order of the Universe, he needs no scientific affirmation of it. At most, he can find some sublime pleasure in the fact that the anthropic principle confirms his beliefs. In his interpretation, purposeful creation belongs to the premise, not to the conclusion of his reasoning. On the other hand, one who believes in the accidental structure of the world has other interpretations of the anthropic principle.

The kind of interpretation presented above is sometimes called the teleological version of the Anthropic Principle. Its adherents usually claim that such a Universe is unique. In fact, one can well argue that the Creator created several universes for a purpose, or, perhaps, for various purposes.

6.09. Is the probability of our existence so low?

Another type of interpretation is the following one. The Universe could have had not only different initial conditions and different physical laws but also a completely different structure of space and time, even a different number of space-time dimensions. Most of these possibilities would exclude the possibility of human existence, and certain ones would exclude even the possibility of any physical causal order. Out of manifold possibilities, one is realized. The probability of the realization of just one out of an infinite number of possibilities is infinitely low. In a mathematical sense, the probability of any realization is close to, or even strictly equal to zero. It is quite improbable that our Universe provides the possibility of human existence, but any other structure of the Universe is equally improbable. The situation bears some resemblance to that situation whereby, out of a mathematical linear segment containing an infinite number of points, one point has to be selected by chance. The a priori probability of selecting any one point is zero, but still, one point is selected. So it is here. If one assumes that, out of innumerable possibilities, something had to become reality, then our quite improbable Universe is no less probable than any other. lf our Universe had not happened to produce any physical intelligent being striving for knowledge, then nobody would have been there to formulate problems and ask questions about the Universe. Because, by chance, the Universe does make our existence possible, we can propose problems; we can ask questions.

As is clearly seen, this view explains the anthropic properties of the Universe in a strictly scientific way, without resorting to any religious beliefs. However, it is based on the assumption that one of the many possibilities had to become a reality; in other words, it assumes that it is necessary that something exist. Without this assumption, the above argument is not complete. The assumption of God's free will, inherent in the religious interpretation, is here replaced with the assumption of the necessity for the existence of something.

But what is real existence? Can an entity that is not aware of its own existence actually be said to exist? Among some physicists there appears the opinion that elementary particles exist only when they are observed (cf. Hibner 1987). Is it not the same with macrocosmic and megacosmic existence? According to Miroslaw Zabierowski (1988), the Anthropic Principle is a direct consequence of modern quantum considerations. It is believed that John Wheeler said for the first time: an observer is necessary for bringing the Universe into existence. It is called the Participatory Version of the Anthropic Principle, but some also call it the strong formulation of the Strong Anthropic Principle.

However, in fact, all our observations are biased because we perform them. The Anthropic Principle states that this bias is so considerable that we are not able to tell whether our existence is an exception or just a common phenomenon (Maddox 1984).

Karol Zieleznik (1991) noticed that the teleological and the participatory versions are not mutually exclusive, and neither follows from the other in a logical way. It means that they are logically independent.

6.10. Existence of many universes

The third possibility is to accept the existence of many universes. The old idea of Everett (1957), introduced to explain some quantum phenomena, is employed to explain a macrocosmic phenomenon - to account for the existence of our Universe with all its peculiar properties. Also, Yakov Borisovich Zeldovich (1981) relates the idea of quantum indeterminism to the concept of many universes. However, the concept can also be discussed without such connections. One can assume all that is possible exists somewhere (in its own space) or that only certain possibilities are actualized. In any case, one can assume that our Universe is not unique. There can be universes with a different number of dimensions, with different signatures of these dimensions, with various laws of physics. If there is an infinite variety of Universes, everything we could have wished could be found among them. The ranges of conditions providing for the existence of intelligent beings are small but finite. Thus, in some of these Universes, conscious beings striving for knowledge could exist, but not in most of them. In the universes where such beings do exist (e.g. in the Universe where we live), we can ask how is it that the existence of life and consciousness is possible. These universes, so to say, know of their existence. In the others, nobody can know anything; there is no intelligence to grasp them. It is no wonder that in just such a peculiar universe as ours all those questions have arisen. They could only have arisen here. According to Davies (1981), in the case of an infinite number of universes, we can only ascertain that our Universe is such as it is, whereas if the Universe were unique, we could exclaim with joy what lucky fellows we are.

The adherents of this interpretation maintain that as it is with universe so it is with almost everything in nature. Nature makes plants produce many seeds, but only few of them actually have an opportunity to germinate. Nature has initiated nuclear reactions in many stars, but heavy elements have been produced in only a few of them. Likewise, nature has created many universes, but only few of them can be aware of their own existence.

The multitude of Universes can most easily be understood by considering that there is a super-space-time in which the space-time of individual universes are somehow located; but one can also conceive of one Universe oscillating through an infinite number of cycles and only once in a while producing conditions conducive to life (Wheeler 1977). Or, one can follow Sacharov's (1980) idea of "multileaf' models of the Universe. Another possibility is that "our Universe" is unique, but it is infinite in time and space, containing space-time domains of an infinite variety of physical conditions. Hoyle called such a universe model the domain universe (Hoyle 1965, 1975; Ellis 1978, 1979). The last possibility creates a bridge between the Anthropic and the Ancient Indian Principles. There are still other variants of understanding a multitude of Universes, some of them connected with the idea of inflationary Universe (cf. Zabierowski 1990).

According to Hawking (1988), the idea of multiple universes or many different domains within our Universe is not consistent with the Strong Anthropic Principle.

He writes:

"There are a number of objections that one can raise to the strong anthropic principle as an explanation of the observed state of the universe. First in what sense can all these different universes be said to exist? If they are really separate from each other, what happens in another universe can have no observable consequences in our own universe. We should therefore use the principle of economy and cut them out of the theory. If on the other hand, they are just different domains of a single universe, the laws of science would have to be the same in each domain, because otherwise one could not move continuously from one domain to another. In this case the only difference between the domains would be their initial configurations and so the strong anthropic principle would reduce to the weak one."

Hawking sees no possibility of fluent transition between two domains of completely different structures.

It is possible to provide further philosophical and fantastic conceptions involving the idea of multiple universes. Some arguments based on the mathematical set theory can lead (using certain assumptions and certain interpretations) to the result that among an infinite number of universes there is also an infinite number of exactly the same universe. If any event (for example, you reading this book) exists within some universe, it must exist in innumerable other universes as wel1 (Barrow and Tipler 1986).

In interpreting the Anthropic Principle using the concept of many universes or many different domains within one universe, the assumption of God's Will or that of necessary existence is replaced with the hypothesis that everything (or at least some kind of everything) possib1e does exist. Perhaps another notion of possibility or of existence should be involved here. Both notions give rise to some basic difficulties but discussing them here would lead us too far afield. It is worthwhile, however, to notice again that it is simply impossible to avoid philosophical issues, even those apparently not related to astronomy or physics, when dealing with cosmological principles....

In the series of considerations presented above (arguments about the exceptional or common character of our Universe, incidental origin or purposeful creation), we not only stand on the frontier of science and metaphysics but also go over to theology. Similar problems were discussed already by Baruch Spinoza (1637-1677) and he eventual1y concluded that to understand God means to understand the Universe and vice versa. However, I wish to comfort all the atheists and agnostics: the God of Spinoza was comprehended in a very abstract or, if you wish to call it so, materialistic way. No minister of any traditional religious organization either in Spinoza's times or at present could accept Spinoza's concept of God.

6.11. Universe and universes

If we want to talk about multiple universes, the question of what a universe (1ower case u) actual1y is must be addressed. As long as we are confronted with just our Universe (capital U, we can keep to the definition that the physical Universe is a system inc1uding everything which physical1y exists. If we allow the existence of many various universes, this definition wil1 no longer be sufficient.

In order to obtain a clear notion of a universe and to be able to distinguish our Universe (capital U) from the others, a fol1owing set of definitions may be used (cf. Rudnicki 1990).

l. universes (small u): sets of domains, each set consisting of all domains of physical existence connected causally to one another in a direct or indirect (e.g. through consecutive partial overlapping) way.

2. Universe (capital 'U'): the universe containing the observable realm of existence.

3. observable realm of existence: the domain causal1y connected directly with human beings.

Definition 3. simply states that to be observable means to be in a causal connection - to be able to exert an influence and to be subject to such influences. This observable realm of existence is the same which was called in the previous parts of this book the observable part of the Universe. The first definition demands that a universe include all domains which are, even in the most indirect sense (consecutive overlapping), connected with one another. Thus the definition rejects any possibility of interaction between two different universes; in other words, it proclaims that two different universes are unobservable by each other. Definition 2 distinguishes our Universe from all the others. These definitions make a distinction between two kinds of unobservability. The parts of our Universe located behind the cosmological horizon are unobservable for us, but a real or imaginary observer located close to our horizon is still able to observe us and those parts simultaneously. He cannot send us any message about the parts unobservable to us or transfer our message to them, but nevertheless he is, in a sense, a connecting link between us and them. A completely different situation exists between two universes. According to Definition l., there could be no such link. If it does exist, then ex definitione the two universes are in fact one universe.

6.12. Can we know anything about other universes?

We come here, in fact, to the limits of logical thinking. This revealed itself fully in a heated argument during the conference "Cosmos" in Venice in May of 1987. D.W. Sciama proposed a proof of the existence of other universes. He said that if our Universe was the only one existing and fulfilled the anthropic principle of purposeful creation, then the numerical values of the physical constants should be optimal (i.e. should be right in the middle of the small range permitted by the anthropic principle). However, if there are many universes with incidental actualization of physical conditions, then, in his opinion, the values of physical constants in our Universe should be dispersed at random within their allowed limits respectively. For the time being, we are not able either to calculate exactly either the limiting values of these intervals or to establish very accurate values of physical constants, but in the future this should be possible. Thus, this is a scientific proposal for the future. The other universes, if they exist, will reveal themselves. We have the experimental (not the observational, just the experimental!) possibility to get information about their existence.

One participant, however, expressed his doubts whether something investigated in our laboratories could be legitimately called another universe because anything that can exert any impact on us belongs ex definitione to our Universe. Another disputant tried to overcome the problem by introducing two separate notions of Universe and Cosmos to distinguish between 'everything that exists and therefore can be investigated in some way' and 'belonging to the same space-time.' Nevertheless, the discussion (or rather both discussions, the official one in the conference room and the other one during the coffee-break) came to a dead end as nobody was able to explain what kind of space-time may be called a universe. The Kaluza-Klein and other models in multidimensional space-time make the problem a rather tricky one. A further question asked in what sense an entity limited to one space-time can or cannot coexist with other similar entities in a super-space-time. The issue of the existence or non-existence of limits of knowledge came out fully (cf. Appendix: Goetheanism in science).

6.13. The Final Anthropic Principle

There are many geometric and physical propositions which are instrumental in understanding the world. Some of them, considered to be more important, go under the name of principles. These include Archimedes' principle, the exclusion principle, the uncertainty principle, the principles of conservation, etc. The Anthropic Principle first used to be included among such general principles also. It was not until the 1980s that one began to talk of the Cosmological Anthropic Principle.

In the book of Barrow and Tipler (1986) discussing this principle as a cosmological one, three versions of the anthropic principle are distinguished. Besides the weak and strong versions, there is a third one, the Final Anthropic Principle. It is provided in the form of a hypothesis which can be briefly expressed as follows:

Every civilization is able to attain a point from where it can not only defend itself from outer and inner perils but can also create (construct) other beings more intelligent and more resistant to the physical condition of the Universe than the members of the civilization themselves (computer construction, genetic engineering. etc.).

Technological products such as computers count as intelligent beings since, as the authors put it, in the behavioristic sense they do act as living, intelligent beings. Such a civilization is capable of conquering ever larger parts of the Universe and in favorable circumstances can get in contact with other civilizations. It can survive up to the moment of the Big Crunch (final singularity) or, if the Universe is to expand forever, survive over enormous cosmic epochs.

6.14. Automata as descendants of men

Here the entire argument is based on the Hubble Law and the Big Bang model. Therefore, since the Big Bang models fall into two classes, there are two possibilities. Either the Universe expands forever and with time tending to infinity the mean density tends to zero; or the total age of the Universe is finite and, after the period of expansion, there is a contraction era terminating in the Big Crunch. In either case, life conditions will change considerably over large cosmic epochs, and today's people or their natural offspring are not likely to persist, even if strong natural evolutionary processes were at work. However, the intelligent beings will be capable of constructing artificial descendants which can live on (i.e. perform purposeful work and construct the next generations of ever more sophisticated automata) in adverse environmental conditions, such as extremely low density of matter (perpetual expansion) or density tending to infinity (Big Crunch).

For a better understanding of the picture presented by the Final Anthropic Principle, let us take into consideration the following. Scholars of the past had a detailed knowledge of their results as well as all the calculations and arguments leading up to them. A scientist of today is an expert in the results obtained and the underlying line of argumentation, but he delegates the burden of arduous calculations to his computer, and, if he uses "library programs," he may well not even understand how those calculations are actually performed. In not too distant future, a scientist will be able to delegate the task of logical argumentation to his computer as well. At some next stage of development, there will be no necessity of scientists knowing the results of investigations, as the computer will produce, record and put them to use by itself when needed. It (he?) will then be wise. The ideal stage will be attained when the computers not only elaborate the results of research but also do scientific research on their own. When we take all this into consideration, the brilliant future predicted by Barrow and Tipler begins to be understandable.

Even if the Universe is to expand forever, generations of more and more sophisticated automata will pass on culture and civilization in the Universe. The only plausible peril could arise if it happens that elementary particles (also protons) have a finite life time.

More promising is a situation when, after the expansion era, there is a period of universal contraction. This would enable neighboring civilizations to come in contact more easily and have an opportunity of exchanging their mutual accumulated experiences, thus increasing their abilities and knowledge enormously. When the Big Crunch, the final singularity, becomes imminent, the civilized and intelligent automata will have unlimited knowledge of everything, possibly even of other universes. And that will be the happy (?) end of human (?) culture and civilization.

The authors of the Final Anthropoid Principle agree with others that the natural evolutionary processes that can produce real observers involve carbon compounds and many other very special circumstances, but they are of the opinion that once human or humanlike beings come into existence and attain a sufficiently high stage of development they are able artificially to construct living and conscious beings from a completely different chemical and physical basis. Those next generations of "scientists" will be, to a large extent, independent of the conditions demanded from the Universe by the first two (weak and strong) versions of the Anthropic Principle.

6.15. Notions of life and consciousness

The promoters of Final Anthropic Principle use the notions of life and consciousness in a sense quite remote from the sense commonly attributed to them. The behaviorist interpretation (definition) given by the authors of Final Principle is utterly materialistic (in the sense of "materialism" that I explained in 3.14). The difficult problem of the nature of life and consciousness, fundamental in most issues related to the Anthropic Principle, is too broad and too serious to be addressed merely as part of the present cosmological considerations. Its essential character should be, nevertheless, stressed here. A few remarks on it will be further provided in the appendix (a.08). Barrow and Tipler propose treating men and automata equally by remarking that every living being, and so every intelligent one, is limited by the laws of physics in the same way that computers are. They do not even refrain from using such notions as soul and eschatology. The software of a computer should be its soul. The issue of eschatology consists of a number of technological problems of existence (of automata) in the exotic physical conditions close to the final singularity.

6.16. The Weak Anthropic Principle as cosmological principle

Let us now discuss what the properties of the three versions of the Anthropic Principle are when accepted as cosmological principles.

The Weak Anthropoid Principle as formulated by its early advocates, Dicke (1961), Karachentsev (1974, 1975), and Carter (1979), was at first conceived not as a cosmological principle but rather as an explanation of why a real observer is necessarily located in a particular place in the Universe (i.e. the terrestrial globe) even though the Copernican Principle remains valid. This purpose, "ecological correction," is particularly distinct in both papers of Karachentsev.

In later formulations, the Weak Anthropic Principle proclaims something concerning solely the observable part of the Universe: its properties can be deduced from the sole fact that Man is there to observe it and that Man could have formed only in this part of the Universe.

As to the unobservable parts of the Universe, the Weak Anthropic Principle requires that they not prevent, in the Earth's vicinity, the development of such laws of nature, numerical values of physical constants, and initial conditions that human beings could come into existence. Apparently, it looks like a negative requirement of the Genuine Copernican Principle, a requirement of not standing in the way of Man's development. However, since "to be unobservable" in contemporary science means "to have no possibility to exert any influence," even a disturbing one, the condition is fulfilled ex definitione by all the unobservable parts of the Universe. It does not describe any additional property of these parts, even in a minimal way, as some of the historical cosmological principles do. So the Weak Anthropic Principle, for all its importance for contemporary astronomy, cannot go by the name of a cosmological principle unless the term cosmological principle is understood as something completely different than it has been to date.

6.17. The Strong Anthropic Principle and the Copernican Principle

The Strong Anthropic Principle refers to the entire Universe and, as such, is a cosmological principle par excellence. The only question is how many properties of the Universe it can predict. The requirement that there be real observers somewhere in the Universe's space-time can be considered fulfilled because the Earth is populated by such observers - us. However, in such an interpretation the Strong Anthropoid Principle turns out to be identical in content to the weak one. Therefore, the Strong Principle is usually understood in that the plural notion of real observers should mean many different "physical conscious beings striving for knowledge" distributed more or less all over the Universe. Only by such an interpretation can this principle be considered to be a cosmological principle at all.

In such a case, it can also be considered as an ecological addition, or, better still, an ecological correction to the Generalized Copernican Principle. Combined, they can be formulated as follows:

The Universe looks (roughly) the same in any direction to an observer located at any point, and in any (large enough) spatial area some real observers can be found in some epoch of its existence.

In fact, if we accept the Copernican Principle, we would have (roughly) the same situation everywhere. If we do not neglect the presence of human or humanlike beings, then the requirement that such beings should not be exceptional in the Universe but should occur throughout it seems quite natural.

6.18. The Strong Anthropic Principle and the Ancient Indian Principle

When discussing the implementation of the Anthropic Principle and the idea of multiple universes, we noted that, in fact, instead of many universes, it would be sufficient to have a unique universe comprised of various domains with random distributions of density of matter, physical constants, physical laws, or even metrics of space-time and number of dimensions. Of course, such domains generally should be large enough to allow the existence of homogeneous sub- domains like the observable region in which we live. There are differing views as to the possibility of the existence of such a universe. We saw already that Hawking argued that if two domains had a different number of dimensions a smooth transition between them would be impossible. However, non-trivial mathematical models involving a gradual change of dimensions are possible. Still easier is to gradually alter signatures of space-time. And, in fact, a gradual transition between different laws of physics is proposed in all theories of unification, like the Grand Unified Theory or Super gravity. Thus, that is not the point. The encountered difficulties are of a different kind.

In the multiple-universe interpretation an infinite number of universes are assumed. Mutatis mutandis, it is the one-heterogeneous-universe interpretation we have to provide for an infinite number of domains. Some should be in expansion, some static, and some collapsing. Only in an infinite number of domains can everything be produced by random variations. Thus, also, humanlike beings can arise by chance. Otherwise, we could still ask why circumstances are so favorable for life and intelligence as they are. The advocates of this interpretation usually have in mind (deliberately or not) a universe fulfilling the Copernican Principle at large. However, in this case it should fulfill three cosmological principles at the same time: Anthropic, Copernican, and Ancient Indian. In principle, a model of a universe can involve any number of cosmological principles, if they do not contradict each other. Here, however, this last condition is not fulfilled. The Indian Principle requires that variability, diversity, and heterogeneity exist in space and in time, in every dimension scale, and also as a mathematical limit in infinity. The Copernican one demands that the Universe should be more and more homogeneous at least when tending to infinity. Therefore a Copernican Universe must either be static in time or originate or end in a singularity. And this property has to be common all over it. Otherwise, the Copernican Principle would be violated. However, it is impossible to reconcile Hubble's Law, for example, with infinite heterogeneity.

The only possibility is to base a model on two principles only: Anthropic and Ancient Indian. Such a model cannot be computed mathematically even using state-of-the-art mathematics, but it still can be perceived mentally as a dim picture. And, in fact, the idea of a universe containing everything is sometimes presented as a picture, although usually an unclear one.

6.19. The Strong Anthropic Principle as cosmological principle

Of course, there is no logical necessity to combine two principles. Let the Copernican and Ancient Indian principles be understood as dealing with large-scale physical objects, celestial bodies, whereas the Anthropic Principle deals with observers of these bodies. This is a reasonable distinction to be made. As was said above, only the Strong Anthropic Principle can be considered a cosmological principle. However, it is not able to produce any mathematical model of the Universe. The logical way from a statement about the existence of conscious beings to the production of a mathematical model of space-time and the properties of matter contained in it is by no means direct, straightforward or short. Nevertheless, this is not an objection to regarding it as a cosmological principle. The Ancient Indian Principle has not produced any mathematical model of the Universe either....

In fact, all the adherents I know of the Anthropic Principle (Strong or Weak) also accept the Generalized Copernican Principle. Only after taking into account the conclusions of the latter (i.e. Hubble's Law and the Big Bang Hypothesis) can some fruitfu1 further conclusions can reached. The formation of chemical elements or physical constants can be deduced, or at least there is a hope of deducing them, after solving the problem of unifying all physical interactions. Barrow and Tipler (1986) confirm this fact in their book, stating frankly (p.368): The 'Big Bang' Theory of the 'origin' and evolution of the Universe is the paradigm of modern cosmology. Sometimes (e.g. Davies 1981) argumentation is provided that Hubble's Law can be derived not only from the Copernican Principle but also directly from the Anthropic Principle, but it can always be shown that these kinds of "proofs" are actually based on assumptions equivalent to the Copernican Principle or Hubble's Law as such; they involve the error of petitio principio.

There are cases in the history of cosmology when two cosmological principles have been applied simultaneously. The world model of Tycho Brahe followed from both the Ancient Greek and the Genuine Copernican Principles and was not easily derived from either one alone. The Strong Anthropic Principle cannot replace all the other principles but can be of interest as a supplement to at least one of them. Of course, it is still too early to assess how important this "ecological correction" is or how permanent the conclusions deduced from it will be. So far, the Strong Anthropic Principle makes us think of a novel interpretation of previously known facts, and this alone provides for its importance, regardless of whether it should be given the status of "cosmological principle" or just "principle," or even that of a logical tautology.

6.20. The Final Anthropic Principle as cosmological principle

As opposed to the other principles, the Final Anthropic Principle is formulated as a hypothesis; at a first glance, it seems hardly possible for it to count as a cosmological principle at all. It claims that there are civilizations perpetually arising, developing, and expanding within the Universe. With increasing age, the Universe should become more and more populated with civilizations. Accepting this principle means an outright refutation of the Steady State Model, according to which the Universe, being infinitely old and always the same, civilizations would have had enough time to develop very highly. However, in fact, our civilization is still in a quite primitive stage, and no contact with any other civilization has been established yet.

I would not like to go here into the detail of proving whether or not our civilization is indeed primitive, arguing whether we can be sure that we are not observed by another civilization, etc. I will even avoid the most important point, whether in the Steady State Model the density of the oldest civilizations should actually be so high, or what the average age of a civilization should be. The Steady State Universe expands, and there are no data enabling one to calculate what precedes faster, the expansion of the Universe or the development of an average civilization. These questions, however remarkable, are rather detailed ones.

Even if the Final Anthropic Principle (when accepted) does not exclude the Steady State model in general, it does exclude certain versions of it. And this states something about the unobservable parts of the Universe. Thus there is no good reason for rejecting the Final Anthropic Principle as a cosmological principle....

6.21. Is every hypothesis a cosmological principle?

Any reasonable, even if completely fanciful, hypothesis concerning the entire Cosmos is consistent with some models of the Universe and inconsistent with others. Thus, a hypothesis, when accepted, discriminates between models, and so says something about the unobservable regions of the Universe as well. To put it in a paradoxical way: if I accept the hypothesis that all stars contain some dragons in their nuclei, then I cannot accept any model which states that in the unobservable regions of the Universe there are stars with no dragons. Can it rightly be claimed that the assumption that stars contain dragons in their nuclei is a cosmological principle? What conditions should a statement satisfy to count as a cosmological principle? What is the difference between a cosmological hypothesis and a cosmological principle...?

6.22. Limitations of our knowledge due to the Anthropic Principle

The Perfect Cosmological Principle is full of optimism. By accepting it we are capable of knowing everything. Just opposite is the case with the Anthropic Principle. Our location in space-time is not an average one. We reside in a specific spatial domain and in a specific epoch of cosmic evolution. Thus, we can observe solely phenomena characteristic of that particular stage of evolution which provides for life and, moreover, only those which can to be observed from the particular environment supporting our existence. We may have no idea what remarkable celestial bodies and phenomena exist in other parts of the Universe (where no intelligent beings to observe them can abide) or in remote epochs in the past from which no traces have been found to date. The fact that one has to exist physically prior to perceiving anything imposes limits on our perceptional ability. Barrow and Tipler (1986) see some analogy between this fact and the theorems of G�del and T�ring-Halton.

G�del�s theorem, which concerns mathematical theories, can be expressed in terms of everyday language: In any more developed mathematical theory one can formulate sentences belonging to the theory but whose veracity cannot be either proved or disproved on the basis of the theory's axioms. That is to say, no more developed mathematical theory gives the possibility of deriving all possible theorems belonging to its domain using strict mathematics (formal logical). G�del�s theorem (the validity of which was proved in a strict mathematical way!) frustrated those who had set to formalizing the entirety of mathematics.

The T�ring-Halton theorem states that the construction of a particular computer cannot be fully analyzed using this very computer.

The Anthropic Principle can be put into a form along the same lines: the Universe cannot be grasped in a sensory way in its space-time totality by any physical intelligent beings produced by this very Universe.

This line of argumentation involves the kind of thinking developed in recent centuries and used now in science as the only admissible one. In fact, the knowledge of the full potential of human thought is still rudimentary. The Anthropic Principle seems to impose more absolute limits on human understanding than the "classic" cosmological horizons did. And nevertheless, if we are able to think of the entire Universe, even using that restricted contemporary variety of scientific thinking, we do know something about it. Georg Unger (1991), after discussing the problem from the Goethean standpoint, considers the Anthropic Principle to be nothing more than idle musing of frustrated scientists.

John A. Wheeler in his foreword to Barrow and Tipler's book (1986) writes:

What is the status of the anthropic principle? Is it a theorem? No. Is it a mere tautology, equivalent to the trivial statement 'The universe has to be such as to admit life, somewhere, at some point in its history, because we are here?' No. Is it a proposition testable by its predictions? Perhaps. Then what is the status of the anthropic principle?

And he urges the reader to make his own judgment about this principle.

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Bibliography

© Konrad Rudnicki

Konrad Rudnicki is a professor at Jagiellonian University, Cracow, Poland. He is a member of the Free European Academy of Science (Holland), member of the Commission of Galaxies of the International Astronomical Union and member of the Mathematical-Astronomical Section at the Goetheanum, (Switzerland). Prof. Rudnicki has been Senior Research Fellow at the California Institute of Technology (1965-67), visiting professor at Rice University, USA (1988-89). His areas of interest are: extragalactic astronomy, cosmology, philosophy of science and methodology of science.

Continued in the next issue of SCR.

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