Emergent Probability and the Anthropic Principle
Is Lonergan's account of emergent probability applicable to the anthropic
principle? An affirmative answer would raise questions about an appropriate
human response to the anthropic principle.
Lonergan sees emergent probability as accounting for a world process that involves six generic notions: (1)spatial distribution; (2) absolute numbers; (3) long intervals of time; (4) selection; (5) stability; and (6) development.1 The anthropic principle affirms a relationship between the emergence of human life on planet earth on the one hand, and on the other hand, the extraordinary properties of the cosmic conditions necessary for this emergence.2
To call these properties "extraordinary" is to affirm the
extreme improbability that each of these properties should emerge. Although
"extraordinary" is sometimes understood as "miraculous"
in a theological context, this understanding is not examined here. What
is specifically examined is an understanding of a scientist's notion of
"probability" and its mathematical precision such that might
suggest or even facilitate human response to the anthropic principle. Indeed
one response proposed is that human intelligence is needed for the survival
of life and matter in the universe to counteract the forces of entropic
This proposal is presented in great mathematical detail by Dr. Frank
J. Tipler, professor of mathematical physics at Tulane University.3
Tipler refers to a book published eight years earlier entitled "The
Anthropic Cosmological Principle" that he had co-authored with his
colleague John D. Barrow. And two years before this, Barrow had published
a popular paperback entitled "The Left Hand of Creation: The Origin
and Evolution of the Expanding Universe" where he refers to the work
of Abbe Georges Lemaistre about the primeval atom.4
Lemaistre describes how this atom exploded in a "big bang" into
the present universe: the primeval atom evolved into galaxies, stars, planets
Did astrophysicists and other humans also evolve from the Big Bang as did galaxies, stars and planets? Yes, at least as regards their brain cells made up of elementary particles that came into existence shortly after the Big Bang. We would not have the knowledge that we have now if astrophysicists had no brain cells made up of these particles. All these were cooked up in the high temperatures generated by the tremendous energies of the primeval atom. There is a sense in which these energies included "conscious energy" as expressed by Joseph P. Provenzano in a book entitled "The Philosophy of Conscious Energy."5
Provenzano convincingly bases this expression on Teilhard's innovative concept of energy as having not only a "tangential" component but also a "radial" component.6 This radial energy is empirically observable through the "generalized empirical method" of Lonergan.7 According to this method, data of inner consciousness are just as empirical as data from external senses. This is implicit in Einstein's "thought experiments." Furthermore, data on radial energy need not be restricted by the lower limit set by quantum indeterminacy; this lower limit masks the haziness of data8 on the tangential energies observed in matter and radiation at microcosmic levels. Teilhard's new parameter of "complexity-consciousness"9 corresponds to the tangential-radial composition of energy. This parameter seems to anticipate a deeper analysis of the complexity of world process. For world process is characterized by the six generic notions listed above: (1) spatial distribution; (2) absolute numbers; (3) long intervals of time; (4) selection; (5) stability; and (6) development.
1. SPATIAL DISTRIBUTION
Matter is distributed throughout space that is unimaginably large. To imagine a distance of billions of light-years requires one to imagine light travelling as centuries go on and on beyond one's life-span from birth to death. Moreover, there are stars clustered into galaxies so many light-years in diameter, and there are zillions of such clusters scattered all over space. And yet, large as space is, it is mostly empty space. The galaxies, stars and planets do not even begin to fill it. Our nearest neighboring star Alpha Centauri is four light-years away, and there is nothing in between except the light it is radiating. The distribution of matter is mostly concentrated in small clusters due to the gravitational attraction between chunks of matter. Although this attraction is somewhat weakened by the expansion of the universe, it remains that space is largely empty.
2. ABSOLUTE NUMBERS
The number of galaxies, stars and atoms is simply staggering. Each galaxy is itself composed of zillions of stars, each star of zillions of atoms, each atom of many elementary particles. The names of the smallest units or groups are: atoms, baryons, bosons, electrons, fermions, gluons, hadrons, leptons, mesons, neutrons, neutrinos, photons, quarks, rishons, sleptons, tauons, W-bosons, X-bosons, Z-bosons, and many others.10 Do these large numbers have any meaning for human intelligence? If so, can the meaning evoke the response proposed explicitly by Tipler, implicitly by Barrow and Lemaistre, and mystically by Teilhard?
3. LONG INTERVALS OF TIME
The Big Bang is now calculated to have occurred at least 12 billion years ago. During that time, matter emerged and evolved in roughly three stages. The first stage was inanimate matter, as small as neutrinos and as large as galaxies . On planet earth, only water, dry land and atmosphere existed, but no life. The second stage was the emergence of life, first plants and then animals. At the third stage, human life emerged. A stage that has emerged fulfilled conditions for a later stage to emerge with some probability. It may or may not survive, depending upon conditions that measure the probability of its survival. A probability of one in a million possibilities is equivalent to a probability of one million in a million million successive possibilities. Thus for matter, life and intelligence to survive on planet earth requires a long succession of possibilities, a long interval of time, perhaps 12 billion years or more.
From a mathematical combination of probabilities of emergence and probabilities of survival, there arises a classification of four classes of developing stages: common and enduring, common and fleeting, rare and fleeting, rare and enduring.11 Molecules are now common, some are enduring but others are fleeting. Many living species are common but some are now endangered and may not endure under certain environmental conditions. Intelligent life is relatively rare in the universe, and it is not yet known to science if the human species will be enduring or fleeting; the fictional "Planet of the Apes" expresses a vague fear that it will be fleeting. But this presumption may be reversed if human consciousness is found to have a decisive role in the survival of life and matter in the universe.12
The organic compounds (carbon, hydrogen, oxygen and nitrogen) are stable and thus increases the probability of life to survive. Radioactive isotopes like uranium and plutonium are unstable. They are not necessary for life, but they are sometimes used as alternative sources of energy. Whether this promotes or endangers life depends upon conditions that are still under investigation.
If world process is 100% stable, it stagnates. But if this is less than 100%, be it ever so slightly less, an increasing probability emerges that it will progress (or decline), evolve (or devolve). Hence arises the generic notion of development, whether positive or negative, depending upon the probabilities of emergence and of survival of earlier schemes. An early scheme with a high probability of emergence fulfills conditions on which later schemes can depend. If its probability of survival is low, it will readily surrender its materials to give later schemes the opportunity to emerge. Thus a sequence of schemes over a span of billions of years from the Big Bang to the rise of human consciousness can be studied as a world process involving spatial distribution, absolute numbers, long intervals of time, selection, stability and development. It can be studied from the viewpoit of emergent probability.
The anthropic principle is here considered as a subset of world process. It affirms that (A) each of the many properties discovered in world process is extremely improbable, but (B) each is a necessary condition for the emergence of human life and observers. By combining and condensing (A) and (B), the question can now be rephrased thus: what extraordinary properties of developing matter lead to the probable emergence of the elementary particles that constitute the human brain?
Let the term "scheme K" denote one such property of developing matter. Lonergan's account of emergent probability includes a scheme K described as follows:
Consider a set of events of the types A, B, C,... and a world situation in which they possess respectively the probabiities p, q, r, ... Then by a general rule of probability theory, the probability of occurrence of all the events in the set will be the product pqr ...of their respective probabilities. Now let us add a further assumption. Let us suppose that the set of events A, B, C, ... satisfies a conditioned scheme of recurrence, say K, in a world situation in which scheme K is not functioning, but in virtue of the fulfillment of prior conditions could begin to function. Then, if A were to occur, B would occur. If B were to occur, C would occur. If C were to occur, ... A would occur. In bried, if any of the events in the set were to occur, then, other things being equal, the rest of the events in the set would follow. In this case we may suppose that the probabilities of the single events are respectively the same as before, but we cannot suppose that the probability of the combination of all events in the set is the same as before. As is easily to be seen, the concrete possibility of a scheme beginning to function shifts the probability of the combination from the product pqr... to the sum p+q+r+... For in virtue of the scheme, it now is true that A and B and C and ... will occur, if either A or B or C or ... occurs; and by a general rule of probability theory, the probability of a set of alternatives is equal to the sum of the probabilities of the alternatives. Now a sum of a set of proper fractions p, q. r. ... is always greater than the product of those same fractions. But a probability is a proper fraction. It follows that, when the prior conditions for the functioning of a scheme of recurrence are satisfied, then the probability of the combinations of events constitutive of the scheme leaps from a product of fractions to a sum of fractions.13
This leap from product to sum of fractions can be illustrated with simple arithmetic. Let A, B, and C each have the probability of 1/5. The product 1/5 x 1/5 x 1/5 = 1/125 or 0.08%. The sum 1/5 + 1/5 + 1/5 = 3/5 or 60%. Thus, if scheme K is functioning, it increases the probability of the set of events A, B, C, ... from 0.08% to 60%.
Thus, if the Big Bang can be assumed to include scheme K, the low probability of each of the individual elementary particles that constitute the human brain will be offset by a high probability of emergence of the human brain. How is this assumption to be verified? This Herculean task will not be attempted here except to indicate in a general way how such a task may be undertaken. It will require the calculation of the probabilities of millions of particles produced by the Big Bang beginning from its first moment to as recently as a million years ago when a human brain first appeared. That it did appear is an indication that a scheme K has been functioning.
What are the properties of this scheme K? Are they "extraordinary"? Can they collectively constitute a general concept possibly under the label of "self-organization"? Self-organization has rapidly grown into an insightful paradigm in studies of development. In a symposium organized by the Vatican Observatory, this paradigm was widely discussed in many statements, of which here are three examples:
... biological self-organization is only possible in the context of non-equilibrium physics.14
The present results of the new paradigm of self-organization show unambiguously that the process of molecular self-organization is essentially subject to certain principles of selection and optimization...15
Self-organization is first of all a factor in physical and chemical processes, not simply an element in living systems.16
These statements suggest that Lonergan's scheme K, seen as a paradigm of self-organization, can function in a variety of ways. More generally, they suggest a relationship between emergent probability and the anthropic principle. This then raises the question about an appropriate human response. One proposed response is that human intelligence be used to promote the survival of the universe against the forces of entropic decline. Human intelligence has discovered a scheme K functioning as a paradigm of self-organization. Human intelligence can now use this discovery for promoting the survival of the universe. How?
Two ways are conceivable, a negative way and a positive way. The negative way is resistance against the entropic forces of decline. Entropy is associated with the Second Law of Thermodynamics that states that, in a closed system, mechanical energy eventually disappears.17 Since this is based on data from laboratory experiments only with closed systems of tangential energy, entropy has nothing to say about radial energy nor can it say a priori that a proposed system of energy, with both its tangential and radial components, would necessarily be a closed system.
The positive way would involve Lonergan's generalized empirical method of testing18 the insights analyzed in "Chaos and Complexity: Scientific Perspectives on Divine Action" published by the Vatican Observatory. The subtitle points to a system that is open to divine action. It suggests that human intelligence is equipped to understand the scientific perspectives where divine action may be infusing radial (or conscious) energy into the system, namely, in those areas of human knowledge about complex processes revealed by mathematics, physics, chemistry and biology.19 Their complexity now appears chaotic to many human minds, including the fourteen contributors to this book, and there is as yet no clear consensus about them.
The dialogue between these fourteen minds is both encouraging and challenging. By publishing it in all its convergent and divergent details, the dialogue can now be broadened to include the entire world of scholarship, especially theology, physics and mathematics. Such a dialogue can grow into a global thought experiment in search of ways of promoting self-organization in the universe, possibly through the radial energy of revelatory information infused from inside and outside this system. There is need to promote the functioning of scheme K in the system and thus keep it open to radial energy.
1 Bernard Lonergan, Insight: A Study of Human Understanding.
Vol.3 of Collected Works of Bernard Lonergan, ed. by F. E. Crowe
and R. M. Doran (Toronto: University of Toronto Press, 1992), 144-48.
1 Bernard Lonergan, Insight: A Study of Human Understanding. Vol.3 of Collected Works of Bernard Lonergan, ed. by F. E. Crowe and R. M. Doran (Toronto: University of Toronto Press, 1992), 144-48.
2 John D. Barrow and Joseph Silk, The Left Hand of Creation. (London: Unwin Paperbacks, 1985), 233.
3 Frank J. Tipler, The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead. (New York: Doubleday, 1994), 7, 8. Tipler systematically limits himself to the language of physics and mathematics, thus isolating his context from the broader context of scholarly and interdisciplinary dialogue. (For example, "intelligence" for him means computerized operations that pass the Turing Test on pages 36-43.) His style of presentation is somewhat counter-productive.
4 Left Hand of Creatiion, 7, 8.
5 Referenced in http://www.smartlink.net/~joepro/bookinfo.html .
6 Teilhard de Chardin, The Phenomenon of Man. (New York: Harper Torchbook Edition, 1961), 64-66.
7 Insight, 95-96.
8 Ibid. 158.
9 Phenomenon, 299-301.
10 Left Hand of Creation, passim.
11 Insight, 146.
12 This is the central position in Tipler's The Physics of Immortality.
13 Insight, 143-44.
14 Chaos and Complexity: Scientific Perspectives on Divine Action, ed. by R. J. Russell, N. Murphy & A. R. Peacocke, (Vatican City: Vatican Observatory Foundation, 1997), 19.
15 Ibid. 105.
16 Ibid. 183.
17 Left Hand of Creation. 19-20.
18 Since the empirical principle includes not only data from the outer senses but also data from inner consciousness, nothing in this principle can arbitrarily exclude the data of faith experiences nor of a method of testing and verifying them empirically. Stoeger would admit that such data cannot be ruled out by the empirical principle, but believes that "they have never been observed" (in Chaos and Complexity, 27). He would therefore rule out reports of mystical experiences of Ignatius of Loyola, John of the Cross, Teresa of Avila and many others in earlier millenia..
19 Chaos and Complexity, passim.