1.2 Anthropic Definitions
From: The Cosmological Anthropic Principle
John Barrow and Frank Tipler,
Oxford University Press 1988
ISBN 0-19-282147-4
"Definitions are like belts. The shorter they are, the
more elastic they need to be." S. Toulmin
Although the Anthropic Principle is widely cited and has often
been discussed in the astronomical literature, (as can be seen
from the bibliography to this chapter alone), there exist few
attempts to frame a precise statement of the Principle; rather,
astronomers seem to like to leave a little flexibility in its
formulation perhaps in the hope that its significance may thereby
more readily emerge in the future. The first published discussion
by Carter saw the introduction of a distinction between what
he termed 'Weak' and 'Strong' Anthropic statements. Here, we
would like to define precise versions of these two Anthropic
Principles and then introduce
Wheeler's Participatory Anthropic Principle' together with
a new Final Anthropic Principle which we shall investigate in
Chapter 10.
The Weak Anthropic Principle (WAP) tries to tie a precise
statement to the notion that any cosmological observations made
by astronomers are biased by an all-embracing selection effect:
our own existence. Features of the Universe which appear to us
astonishingly improbable, a priori, can only be judged in their
correct perspective when due allowance has been made for the
fact that certain properties of the Universe are necessary if
it is to contain carbonaceous astronomers like ourselves. This
approach to evaluating unusual features of our Universe first
re-emerges in modern times in a paper of Whitrow" who, in
1955, sought an answer to the question 'why does space have three
dimensions?'. Although unable to explain why space actually has,
(or perhaps even why it must have), three dimensions, Whitrow
argued that this feature of the World is not unrelated to our
own existence as observers of it. When formulated in three dimensions,
mathematical physics possesses many unique properties that are
necessary prerequisites for the existence of rational information-processing
and 'observers' similar to ourselves. Whitrow concluded that
only in three-dimensional spaces can the dimensionality of space
be questioned. At about the same time Whitrow also pointed out
that the expansion of the Universe forges an unbreakable link
between its overall size and age and the ambient density of material
within it.16 This connection reveals that only a very 'large'
universe is a possible habitat for life. More detailed ideas
of this sort had also been published in Russian by the Soviet
astronomer Idlis." He argued that a variety of special astronomical
conditions must be met if a universe is to be habitable. He also
entertained the possibility that we were observers merely of
a tiny fraction of a diverse and infinite universe whose unobserved
regions may not meet the minimum requirements for observers that
there exist hospitable temperatures and stable sources of stellar
energy.
Our definition of the WAP is motivated in part by these insights
together with later, rather similar ideas of Dicke" who,
in 1957, pointed out that the number of particles in the observable
extent of the Universe, and the existence of Dirac's famous Large
Number Coincidences 'were not random but conditioned by biological
factors'. This motivates the following definition:
Weak Anthropic Principle (WAP): The observed values of all
physical and cosmological quantities are not equally probable
but they take on values restricted by the requirement that there
exist sites where carbon-based life can evolve and by the requirement
that the Universe be old enough for it to have already done so.
Again we should stress that this statement is in no way either
speculative or controversial. It expresses only the fact that
those properties of the Universe we are able to discern are self-selected
by the fact that they must be consistent with our own evolution
and present existence. WAP would not necessarily restrict the
observations of non-carbon-based life but our observations are
restricted by our very special nature. As a corollary, the WAP
also challenges us to isolate that subset of the Universe's properties
which are necessary for the evolution and continued existence
of our form of life. The entire collection of the Universe's
laws and properties that we now observe need be neither necessary
nor sufficient for the existence of life. Some properties, for
instance the large size and great age of the Universe, do appear
to be necessary conditions; others, like the precise variation
in the distribution of matter in the Universe from place to place,
may not be necessary for the development of observers at some
site. The non-teleological character of evolution by natural
selection ensures that none of the observed properties of the
Universe are sufficient conditions for the evolution and existence
of life.
Carter, and others, have pointed out that as a self-selection
principle the WAP is a statement of Bayes' theorem. The Bayesian
approach" to inference attributes a priori and a posteriori
probabilities to any hypothesis before and after some piece of
relevant evidence, E, is taken into account. In such a situation
we call the before and after probabilities p, and PA, respectively.
The fact that for any particular outcome 0, the probability of
observing 0 before the evidence E is known equals the probability
of observing 0 given the evidence E, after E was accounted for,
is expressed by the equation,
(1. 1)
where/ denotes a conditional probability. Bayes' formula"
then gives the relative plausibililty of any two theories a and
0 in the face of a piece of evidence E as
(1.2)
Thus the relative probabilities of the truth of or are modified
by the conditional probabilities and which account for any bias
of the experiment (or experimenter) towards gathering evidence
that favours a rather than 0 (or vice versa). The WAP as we have
stated it is just an application of Bayes' theorem. The WAP is
certainly not a powerless tautalogical statement because cosmological
models have been defended in which the gross structure of the
Universe is predicted to be the same on the average whenever
it is observed. The, now defunct, continuous creation theory
proposed by Bondi, Gold and Hoyle is a good example. The WAP
could have been used to make this steady-state cosmology appear
extremely improbable even before it came into irredeemable conflict
with direct observations. As Rees points out:
the fact that there is an epoch when [the Hubble time, tH
which is essentially equal to the age of the Universe] is of
order the age of a typical star..... is not surprising in any
'big bang' cosmology. Nor is it surprising that we should ourselves
be observing the universe at this particular epoch. In a steady-state
cosmology, however, there would seem no a priori reason why the
timescale for stellar evolution should not be either [much less
than] tH (in which case nearly all the matter would be in dead
stars or 'burnt-out' galaxies) or [much greater than] t, (in
which case only a very exceptionally old galaxy would look like
our own). Such considerations could have provided suggestive
arguments in favour of 'big bang' cosmologies ...
We can also give some examples of how the WAP leads to synthesizing
insights that deepen our appreciation of the unity of Nature.
Observed facts, often suspected at first sight to be unrelated,
can be connected by examining their relation to the conditions
necessary for our own existence and their explicit dependence
on the constants of physics. Let us reconsider, from the Bayesian
point of view, the classic example mentioned in section 1.1,
relating the size of the Universe to the period of time necessary
to generate observers. The requirement that enough time pass
for cosmic expansion to cool off sufficiently after the Big Bang
to allow the existence of carbon ensures that the observable
Universe must be relatively old and so, because the boundary
of the observable Universe expands at the speed of light, very
large. The nuclei of carbon, nitrogen, oxygen and phosphorus
of which we are made, are cooked from the light primordial nuclei
of hydrogen and helium by nuclear reactions in stellar interiors.
When a star nears the end of its life, it disperses these biological
precursors throughout space. The time required for stars to produce
carbon and other bioactive elements in this way is roughly the
lifetime of a star on the 'main-sequence' of its evolution, given
by (1.3)
where G is Newton's gravitation constant, c is the velocity of
light, h is Planck's constant and mN is the proton mass. Thus,
in order that the Universe contain the building-blocks of life,
it must be at least as old as t* and hence, by virtue of its
expansion, at least ct* (roughly ten billion light years) in
extent. No one should be surprised to find the Universe to be
as large as it is. We could not exist in one that was significantly
smaller. Moreover, the argument that the Universe should be teeming
with civilizations on account of its vastness loses much of its
persuasiveness: the Universe has to be as big as it is in order
to support just one lonely outpost of life. Here, we can see
the deployment of (1.2) explicitly if we let the hypothesis that
the large size of the Universe is superfluous for life on planet
Earth be a and let hypothesis 0 be that life on Earth is connected
with the size of the Universe. If the evidence E is that the
Universe is observed to be greater than ten billion light years
in extent then, although << 1, the hypothesis is not necessarily
then improbable because we have argued that ~ 1. We also observe
the expansion of the Universe to be occurring at a rate which
is irresolvably close to the special value which allows it the
smallest deceleration compatible with indefinite future expansion.
This feature of the Universe is also dependent on the epoch of
observation. And again, if galaxies and clusters of galaxies
grow in extent by mergers and hierarchical clustering,' then
the characteristic scale of galaxy clustering that we infer will
be determined by the cosmic epoch at which it is observed.
Ellis has stressed the existence of a spatial restriction
which further circumscribes the range of observed astronomical
phenomena. What amounts to a universal application of the principle
of natural selection would tell us that observers may only exist
in particular regions of a spatially inhomogeneous universe.
Since realistic mathematical models of inhomogeneous universes
are extremely difficult to construct, various unverifiable cosmological
'Principles' are often used by theoretical cosmologists to allow
simple cosmological models to be extracted from Einstein's general
theory of relativity. These Principles invariably make statements
about regions of the Universe which are unobservable not only
in practice but also in principle (because of the finite speed
of light). Principles of this sort need to be used with care.
For example, Principles of Mediocrity like the Copernican Principle
or the Principle of Plenitude (see Chapter 3) would imply that
if the Universe did possess a preferred place, or centre, then
we should not expect to find ourselves positioned there. However,
general relativity allows possible cosmological models to be
constructed which not only possess a centre, but which also have
conditions conducive to the existence of observers only near
that centre. The WAP would offer a good explanation for our central
position in such circumstances, whilst the Principles of Mediocrity
would force us to conclude that we do not exist at all! According
to WAP, it is possible to contemplate the existence of many possible
universes, each possessing different defining parameters and
properties. Observers like ourselves obviously can exist only
in that subset containing universes consistent with the evolution
of carbon-based life.
This approach introduces necessarily the idea of an ensemble
of possible universes and was suggested independently by the
Cambridge biologist Charles Pantin in 1965. Pantin had recognized
that a vague principle of amazement at the fortuitous properties
of natural substances like carbon or water could not yield any
testable predictions about the World, but the amazement might
disappear if4ll
we could know that our Universe was only one of an indefinite
number with varying properties, [so] we could perhaps invoke
a solution analogous to the principle of Natural Selection; that
only in certain universes which happen to include otirs, are
the conditions suitable for the existence of life, and unless
that condition is fulfilled there will be no observers to note
the fact
However, as Pantin also realized, it still remains an open
question as to why any permutation of the fundamental constants
of Nature allows the existence of life, albeit a question we
would not be worrying about were such a fortuitous permutation
not to exist. If one subscribes to this 'ensemble interpretation'
of the WAP one must decide how large an ensemble of alternative
worlds is to be admitted. Many ensembles can be imagined according
to our willingness to speculate-different sets of cosmological
initial data, different numerical values of fundamental constants,
different space-time dimensions, different laws of physics-some
of these possibilities we shall discuss in later chapters.
The theoretical investigations initiated by Carter' reveal
that in some sense the subset of the ensemble containing worlds
able to evolve observers is very 'small'. Most perturbations
of the fundamental constants of Nature away from their actual
numerical values lead to model worlds that are still-born, unable
to generate observers and become cognizable. Usually, they allow
neither nuclei, atoms nor stars to exist. Whatever the size and
variety of permutations allowed within a hypothetical ensemble
of 'many worlds', one might introduce here an analogue of the
Drake equation" often employed to guess the number of extraterrestrial
civilizations in our Galaxy. Instead of expressing the probability
of life existing elsewhere as a product of independent probabilities
for the occurrence of processes like planetary formation, protocellular
evolution and so forth, one could express the probability of
life existing anywhere as a product of probabilities that encode
the fact that life is only possible if parameters like the fine
structure constant or the strong coupling constant lie in a particular
numerical range."" The existence of the fundamental
cosmic timescale like (1.3), fixed only by invariant constants
of Nature, c, h, G, and m,, was exploited by Dicke to produce
a powerful WAP argument against Dirac's conclusion that the Newtonian
gravitation constant, G, is decreasing with time. Dirac had noticed
that the dimensionless measure of the strength of gravity
(1.4)
is roughly of order the inverse square root of the number
of nucleons in the observable Universe, N(t), at the present
time t,) 1 O'o yrs. At any time, t, the quantity N(t) is simply
(1.5)
if we use the cosmological relation that the density of the
Universe, p,, is related to its age by pu (Gt2)-i. (The present
age of roughly 10")yrs is displayed in the last step.) Dirac
argued that it is very unlikely that these two quantities should
possess simply related dimensionless magnitudes which are both
so vastly different from unity and yet be independent. Rather,
there must exist an approximate equality between them of the
form
(1.6)
However, whereas ac, is a time-independent combination of
constants, N(t) increases linearly with the time of observation,
t, which for us is the present age of the Universe. The relation
(1.6) can only hold for all times if one component of a, is time-varying
and so Dirac suggested that we must have . The quantities N(t)
and are now observed to be of the same magnitude because (as
a result of some unfound law of Nature) they are actually equal,
and furthermore, they are of such an enormous magnitude because
they both increase linearly in time and the Universe is very
old-although this 'oldness' can presumably only be explained
by the WAP even in this scheme of 'varying' constants for the
reasons discussed above in connection with the size of the Universe.
However, the WAP shows Dirac's radical conclusion of a time-varying
Newtonian gravitation constant to be quite unnecessary. The coincidence
that today we observe N-a-, 2 is necessary for our existence.
Since we would not expect to observe the Universe either before
stars form or after they have burnt out, human astronomers will
most probably observe the Universe close to the epoch t* given
by (1.3). Hence, we will observe the time-dependent quantity
N(t) to take on a value of order N(t*) and, by (1.3) and (1.4),
this value is necessarily just
(1.7)
where the second relation is a consequence of the value of
t, in (1.3). If we let delta be Dirac's hypothesis of time-varying
G, while beta is the hypothesis that G is constant while the
'evidence', E, is the coincidence (1.6); then, although the a
priori probability that we live at the time when the numbers
N(t) and are equal is very low, << 1), this does not render
hypothesis beta (the constancy of G) implausible because there
is an anthropic selection effect which ensures ~ 1. This selection
effect is the one pointed out by Dicke. We should notice that
this argument alone explains why we must observe N(t) and to
be of equal magnitude, but not why that magnitude has the extraordinarily
large value _ 1 079. (We shall have a lot more to say about this
problem in Chapters 4, 5 and 6). As mentioned in section 1.1,
Carter' introduced the more speculative Strong Anthropic Principle
(SAP) to provide a 'reason' for our observation of large dimensionless
ratios like 1071; We state his SAP as follows:
Strong Anthropic Principle (SAP): The Universe must have those
properties which allow life to develop within it at some stage
in its history.
An implication of the SAP is that the constants and laws of Nature
must be such that life can exist. This speculative statement
leads to a number of quite distinct interpretations of a radical
nature: firstly, the most obvious is to continue in the tradition
of the classical Design Arguments and claim that:
(A) There exists one possible Universe 'designed' with the
goal of generating and sustaining 'observers'.
This view would have been supported by the natural theologians
of past centuries, whose views we shall examine in Chapter 2.
More recently it has been taken seriously by scientists who include
the Harvard chemist Lawrence Henderson' and the British astrophysicist
Fred Hoyle, so impressed were they by the string of 'coincidences'
that exist between particular numerical values of dimensionless
constants of Nature without which life of any sort would be excluded.
Hoyle points out
how natural it might be to draw a teleological conclusion
from the fortuitous positioning of nuclear resonance levels in
carbon and oxygen:
I do not believe that any scientist who examined the evidence
would fail to draw the inference that the laws of nuclear physics
have been deliberately designed with regard to the consequences
they produce inside the stars. If this is so, then my apparently
random quirks have become part of a deep-laid scheme. If not
then we are back again at a monstrous sequence of accidents.
The interpretation (A) above does not appear to be open either
to proof or to disproof and is religious in nature. Indeed it
is a view either implicit or explicit in most theologies. This
is all we need say about the 'teleological' version of the SAP
at this stage. However, the inclusion of quantum physics into
the SAP produces quite different interpretations. Wheeler' has
coined the title 'Participatory Anthropic Principle' (PAP) for
a second possible interpretation of the SAP:
(B) Observers are necessary to bring the Universe into being.
This statement is somewhat reminiscent of the outlook of Bishop
Berkeley and we shall see that it has physical content when considered
in the light of attempts to arrive at a satisfactory interpretation
of quantum mechanics." It is closely related to another
possibility:
(C) An ensemble of other different universes is necessary
for the existence of our Universe.
This statement receives support from the 'Many-Worlds' interpretation
of quantum mechanics and a sum-over-histories approach to quantum
gravitation because they must unavoidably recognize the existence
of a whole class of real 'other worlds' from which ours is selected
by an optimizing principle." We shall express this version
of the SAP mathematically in Chapter 7, and we shall see that
this version of the SAP has consequences which are potentially
testable. Suppose that for some unknown reason the SAP is true
and that intelligent life must come into existence at some stage
in the Universe's history. But if it dies out at our stage of
development, long before it has had any measurable non-quantum
influence on the Universe in the large, it is hard to see why
it must have come into existence in the first place. This motivates
the following generalization of the SAP:
Final Anthropic Principle (FAP): Intelligent information-processing
must coine into existence in the Universe, and, once it comes
into existence, it will never die out.
We shall examine the consequences of the FAP in our final chapter
by using the ideas of intormation theory and computer science.
The FAP will be inade precise in this chapter. As we shall see,
FAP will turn out to require the Universe and elementary particle
states to possess a number of definite properties. These properties
provide observational tests for this statement of the FAP. Although
the FAP is a statement of physics and hence ipso facto"
has no ethical or moral content, it nevertheless is closely connected
with moral values, for the validity of the FAP is the physical
precondition for moral values to arise and to continue to exist
in the Universe: no moral values of any sort can exist in a lifeless
cosmology. Furthermore, the FAP seems to imply a melioristic
cosmos. We should warn the reader once again that both the FAP
and the SAP are quite speculative; unquestionably, neither should
be regarded as well-established principles of physics. In contrast,
the WAP is just a restatement, albeit a subtle restatement, of
one of the most important and well-established principles of
science: that it is essential to take into account the limitations
of one's measuring apparatus when interpreting one's observations.
Roger Penrose on the Anthropic Principle (from The Emperor's
New MInd)
How important is consciousness for the universe as a whole?
Could a universe exist without any conscious inhabitants whatever'?
Are the laws of physics specially designed in order to allow
the existence of conscious life? Is there something special about
our particular location in the universe, either in space or in
time? These are the kinds of question that are addressed by what
has become known as the anthropic principle. This principle has
many forms. (See Barrow and Tipler 1986.) The most clearly acceptable
of these addresses merely the spatiotemporal location of conscious
(or 'intelligent') life in the universe. This is the weak anthropic
principle. The argument can be used to explain why the conditions
happen to be just right for the existence of (intelligent) life
on the earth at the present time. For if they were not just right,
then we should not have found ourselves to be here now, but somewhere
else, at some other appropriate time. This principle was used
very effectively by Brandon Carter and Robert Dicke to resolve
an issue that had puzzled physicists for a good many years. The
issue concerned various striking numerical relations that are
observed to hold between the physical constants (the gravitational
constant, the mass of the proton, the age of the universe, etc.).
A puzzling aspect of this was that some of the relations hold
only at the present epoch in the earth's history, so we appear,
coincidentally, to be living at a very special (line (give or
take a few million years!). This was later explained, by Carter
and Dicke, by the fact that this epoch coincided with the lifetime
of what are called main-sequence stars, such as the sun. At any
other epoch, so the argument ran, there would be no intelligent
life around in order to measure the physical constants in question-so
the coincidence had to hold, simply because there would be intelligent
life around only at the particular time that the coincidence
did hold! The strong anthropic principle goes further. In this
case, we are concerned not just with our spatio-temporal location
within the universe, but within the infinitude of possible universes.
Now we can suggest answers to questions as to why the physical
constants, or the laws of physics generally, are specially designed
in order that intelligent life can exist at all. The argument
would be that if the constants or the laws were any different,
then we should not be in this particular universe, but we should
be in some other one! In my opinion, the strong anthropic principle
has a somewhat dubious character, and it tends to be invoked
by theorists whenever they do not have a good enough theory to
explain the observed facts (i.e. in theories of particle physics,
where the masses of particles are unexplained and it is argued
that if they had different values from the ones observed, then
life would presumably be impossible, etc.). The weak anthropic
principle, on the other hand, seems to me to be unexceptionable,
provided that one is very careful about how it is used.
By the use of the anthropic principle either in the strong
or weak form-one might try to show that consciousness was inevitable
by virtue of the fact that sentient beings, that is 'we', have
to be around in order to observe the world, so one need not assume,
as I have done, that sentience has any selective advantage! In
my opinion, this argument is technically correct, and the weak
anthropic argument (at least) could provide a reason that consciousness
is here without it having to be favoured by natural selection.
On the other hand, I cannot believe that the anthropic argument
is the real reason (or the only reason) for the evolution of
consciousness. There is enough evidence froni other directions
to convince me that consciousness is of powerful selective advintage,
and I do not think that the anthropic argument is needed.
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