Sunday, December 22, 2013

In His image: Would Yoda have a soul?

What is man, that thou art mindful of him? and the son of man, that thou visitest him?
For thou hast made him a little lower than the angels, and hast crowned him with glory and honour.
Thou madest him to have dominion over the works of thy hands; thou hast put all things under his feet:
All sheep and oxen, yea, and the beasts of the field;
The fowl of the air, and the fish of the sea, and whatsoever passeth through the path
s of the seas.    Psalm 8, v4-8.
Is there intelligent life on other worlds?  A question invariably asked when I was catechizing minimum security prisoners and adult pupils at "Science and the Church" classes,    And if there is, do such beings have souls?

As far as Yoda goes, most people who have seen the Star Wars epics would probably answer "Yes, of course!"... given that Yoda is a hero, cute, and knows how to manipulate THE FORCE to good ends... but then those considerations do not really take into account what the Church has to say about souls:
"The human person, created in the image of God, is a being at once corporeal and spiritual....Man, whole and entire is therefore willed by God...soul refers to the innermost aspect of man, that by which he is most specially in God's image:  'soul' signifies the spiritual principle in is because of the spiritual soul that the body made of matter becomes  a living, human body;  spirit and body in man are not two natures united but rather their union forms a single nature."  Catechism of the Catholic Church, excerpted from paragraphs 362, 363, 365.
Now that is a complete statement, but it doesn't make the properties of a soul explicit.   What do these properties entail--belief in a deity?   a moral/ethical code?   wonder about the meaning of it all?   There is another quote, wrongly attributed to C.S. Lewis, but actually from the science-fiction author, Walter M. Miller, Jr. (author of a "Canticle for Leibowitz") that to me is a satisfactory statement (with properties still left undefined), in agreement with the Catechism:
"You don't have a soul.   You are a soul.   You have a body."
And as Brother Guy Consulagmo, a Vatican astronomer, put it when discussing alien life:
 "Going back to the Middle Ages, the definition of a soul is to have intelligence, free will, freedom to love or not to love, freedom to make decisions...
Finally, here's what C.S. Lewis has to say:
 "By this (rational souls) I include not merely the faculty to abstract and calculate, but the apprehension of values, the power to mean by 'good' something more than 'good for me' or even 'good for my species'." (from Religion and Rocketry in The World's Last Night)
Given that this issue is settled (???), let's move on to the next question: do intelligent extraterrestial beings exist? Are we alone in the universe? The Church as an institution is also interested: in 2009 the Vatican held a week-long conference on the existence of extra-terrestial life.   A number of scientific and religious issues were considered, but no consensus was reached.   We think that alien life would be based on carbon-based biochemistry like that on Earth, but that assumption might not hold.  If it does hold, then to make an estimate we'd need to know how many earth-like planets there are, and then make some estimates of how many of these would develop life, and the probability that such life would become intelligent.  The Drake Equation gives such an estimate for the number of planets in our galaxy, the Milky Way, as between a thousand and hundred million (that's quite a big error limit!).  Many new discoveries of "earth-like" planets are reported: a recent estimate of such in our galaxy is a hundred billion, and a hundred sextillion in the universe. So then the critical links are the probability of life originating on an earth-like planet (or even non-earth like) and the probability of such life developing intelligence.  Shown below are pictures (drawings, not scientific images) of the five most earthlike planets.   We want to emphasize that the properties of these planets are inferred from astronomical data; no astronomical images of planets this small have been observed.

And then we have to consider the Fermi Paradox, "where is everybody?", if such life exists. Why is there no evidence of communication--radio, satellites, whatever--that science-fiction portrays in much detail? Or would intelligent life take other paths than technological? (I ignore flying saucer reports--those are legend and myth.)

Well, let's brush the Fermi Paradox under the rug, and assume that somewhere over the rainbow, outside our solar system, intelligent life exists. Would such life necessarily have souls? And what is the attitude of the Church toward such beings? Would the Church have a mission to save them, as it did in the Americas and Asia?   According to one of the Vatican Observatory astronomers, Brother Guy Consolmagno, the answer is "Yes" : "Any entity - no matter how many tentacles it has - has a soul."
The situation is complex and not to be explained simply by examining the properties of souls listed above.   The most trenchant exposition has been given by C.S. Lewis in his essay, Religion and Rocketry.   Here are the issues to be considered:

  • Do these aliens have a rational soul?   Computers, no matter what their degree of artificial intelligence would not.  (I'm reminded of an anecdote, probably apocryphal, about a world famous computer expert who was giving a seminar on artificial intelligence at an academic institution where I was teaching.    Someone in the audience asked him 'would you want your daughter to marry a computer?'  and another voice shouted out immediately "Why not--his wife did.")
  • If these aliens have rational souls, are they fallen, or are they like Adam and Eve before the Fall, in a state of innocence and grace?   If they are not fallen, would it be appropriate to send missionaries to them?
  • "If all of them (and surely all is a long shot) or any of them have fallen have they been denied Redemption by the Incarnation and Passion of Christ? For of course it is no very new idea that the eternal Son may, for all we know, have been incarnate in other worlds than earth and so saved other races than ours." (quote from Rocketry and Religion.) In the first book of his wonderful speculative fiction trilogy, "Out of the Silent Planet" Lewis considers such alien intelligent beings that have not fallen, innocent and without Original Sin.
  • Lewis considers whether missionary activity to fallen species would be corrupting or  salvational, whether Christ could have appeared to other fallen species, or whether God might have given other forms of Redemption--read the essay from the link for a fuller exposition.
Have we answered the original question?   NO!, but another quote from Religion and Rocketry is apposite:
"If I remember rightly, St. Augustine raised a question about the theological position of satyrs, monopods, and other semi-human creatures. He decided it could wait till we knew there were any. So can this."

Finally, I'll put my own position down--it's exemplified in a fine science-fiction story (science-fiction is my fourth best theological resource, following Holy Scripture, St. Augustine, and St.Thomas Aquinas).   A scientific couple embark on a search through the galaxy for life, any life.   The search proves fruitless, the wife dies, but finally the husband realizes as he is about to die that he is not really alone; in a final epiphany he realizes the truth of Scripture, that the universe has been created by God, and man as the image of God, as in Psalm 8.

Sunday, October 27, 2013

Top-down to Jesus--On bypassing the road to Damascus

Be not afraid of faith: some are born with faith, some achieve faith, and some have faith thrust upon them.” (with apologies to William Shakespeare, Twelfth Night.)
In my very first blog I promised to tell the story of my conversion—how an agnostic Jewish scientist became a Catholic in his senior years, to the horror of many colleagues, the amazement of his family, and the delight of his wife. Conversion stories interest the Catholic faithful (possibly because the missionary impulse that goes with faith is vicariously satisfied). However, in telling this story I have a different focus than auto-biographical, I propose to explore the roots of faith—revelation, grace and rational conviction. The last is not important for some and crucially important for others, but as Pascal pointed out in his wager, rational conviction can lead to grace-filled faith (see “The Pearl of Great Price—Pascal'sWager Revisited).

There is another continuation here: in my second blog, “Belief, Knowledge and Faith”, there was a promise to discuss further the difference between faith and what might be termed “scientific knowledge”. By distinguishing my belief in science from that in the dogma/doctrine of the Catholic Church, I hope to demonstrate the limits of the scientific domain and the unlimited power of rationally based faith.

So, let's begin with the minimum bit of biography. I'm not going to say much about my early religious life, other than I grew up as a secular Jew, despite having several rabbis as great-grandparents. (In the great wisdom of early adolescence, I refused to be Bar-Mitzvah'd, believing it to be a sham ceremony when there was so much misery and injustice in the world, misery and injustice ignored by those fur-coated ladies parading in Temple.) Nevertheless, there was a belief of sorts in a Creator--my teen-age passion was astronomy, visiting the local planetarium and constructing (not well) a six-inch reflecting telescope; I realized instinctively the dictum of Psalm 19A, "The Heavens declare the glory of God". Working during a college summer in the Yosemite forest service, lying underneath one of the big trees, I was filled with awe at the Creator's work here on earth. My wife is Catholic, and we were married in a Catholic church.  But I stayed my distance from the Church, only attending functions at my children's Catholic school and at baptisms (at one of these, for my oldest daughter, I was much embarrassed by being asked to serve as an altar boy for the priest--my protestations that I wasn't Catholic were to no avail).

Now into each life some rain must fall, and fall it did in mine--without going into detail and violating confidences, I'll say that in my 60's I became a member of a Twelve Step Groups--Hi, I'm Bob and I'm  a ______ (fill in the blank);  the presence of a Higher Power (uppercase obligatory), who will help to break addictive chains--alcohol, drugs, food, persons--is a guiding principle of such groups.   I was disposed to believe in the presence of such a Higher Power, but I came to realize that the phrase was doublespeak, Orwellian "sheer cloudy vagueness", a euphemism for God, so I began to search for a more satisfying way to think about the deity (at that time in lowercase).

Fortunately at this point the Holy Spirit intervened (exactly how, this old guy's memory fails), and I was prompted to read "Who Moved the Stone" by Frank Morison, a pseudonym for Albert Henry Ross, a British writer who originally set out to disprove the Resurrection, but who, on evaluating the biblical accounts, came to believe.    I won't recount the evidence (it's detailed more fully in the linked articles), but it seemed to me that an impartial jury (not composed of evangelical atheists) would give a verdict of "innocent", i.e. the arguments that the biblical account of the Resurrection were true.   What struck me even more on going from "Who Moved the Stone" to the the New Testament. was that this bunch of uneducated yahoos--fishermen, tax collectors, women--had managed to out-talk the scholars of Judaism and thereby to spread the Christian faith through the Roman world.   Surely they must have been inspired by encounters with the risen Jesus and the inner voice of the Holy Spirit.   It also occurred to me that if one does believe in the Gospel account of the Resurrection, then one should also credit other
incidents described there, in particular the words of Jesus giving the keys of the Kingdom to Peter, thus founding the Catholic Church.   Accordingly, the Christian religion to which I would convert should be Roman Catholic (this choice also eliminated a certain amount of domestic controversy).  I must emphasize that this whole process was one of rational decision making--no visions, no voices--whence "Top Down to Jesus".   I envy those  who have had visions of our Lord and heard His voice (and I have had first hand accounts of such from some of my friends), but this was not my good fortune.

Of course conversion is an ongoing process--study, service, prayer, adoration, retreats--all the tools and fertilizer to make the fig tree of faith bear ever more fruit.   To fully recount this continuing process would take a book chapter, not a blog.   Much is related or implied in my other blogs and in the biographical note below, but I'll add these brief (?) comments.   First, as a scientist, I had to struggle to believe in miracles--Fr. Mc___'s answer during my initial catechesis to my questions on  points of dogma, "If you believe in one miracle, the Resurrection, why are you having problems with others?" and "If you believe in the possibility, even if you have questions, that is enough."--helped.   As I looked at the evidence for contemporary miracles, particularly that reported by Dr. Alexis Carrell at Lourdes, and read what C.S. Lewis and Ralph McInerny had to say about the reality of miracles, my scientific skepticism waned.     Second, those few non-"Top Down", but "In the Heart" moments where I felt the presence of Deity (not well defined, not as an image or as a voice) have been evoked by music:  Gregorian chant during a retreat at St. Vincent Archabbey, certain hymns and liturgical music, and very, very infrequently, at quiet times in early morning during Adoration or other prayer, when the melody of some favorite hymn would come to mind.

Now I claim that this belief in Jesus and in the dogma/doctrine of the Catholic Church, this faith, is akin in certain respects to and also different from my belief/faith in science.   To begin with let me assert that by no means can science explain everything, that is to say, "scientism" is a false doctrine.   The books of Keith Ward, the writings of Fr. Stanley Jaki (particularly "The Limits of a Limitless Science"), and most recently an essay by the eminent biologist Austin Hughes on "The Folly of Scientism" effectively demolish the positions of the evangelical atheists, Dawkins, Atkins, and (of late) Hawking, who believe that science is the only answer.   They ignore all that science can't explain, the "why" questions;  for example,  they believe that since we can show by functional MRI where the brain is active when we pray or contemplate, we fully understand how and what the mind is doing in prayer or mystical experience.  Wrong!

Most people put the same faith in what science tells them as the Christian faithful did in the dogma of the Church.   How many people have done Galileo's inclined plane experiment to verify laws of motion (which I did in the physics lab at Caltech)...etc.    The essence of the scientific method is that theoretical predictions can be verified by repeated measurements, and this in turn implies that those things and realities that cannot be quantified and realized by an experiment cannot be deal with scientifically.   And even then science is limited in setting up idealized experiments, situations isolated from the surroundings for which the theoretical gedanken experiment may not always be possible.   And of course there is the fundamental incompatibility of the two major theories, quantum mechanics and relativity,  that are the foundation of modern science.    In desperation to avoid the act of creation that implies the Deity, theoretical physicists are putting their faith in multiverse theories, M-theories with infinite landscapes, theories that are most unlikely to be verified  experimentally (i.e. to be capable of being falsified), exercises in mathematical metaphysics, exercises which are even more removed from one's experience than that supposedly put by Medieval theologians: how many angels could stand on the point of a pin (which was, in fact, a reasonable question--how many immaterial entities could be contained in a point).    Indeed, it is clear that the lucid framework of physical science cannot even support  all the occurrences in our everyday experience--the butterfly wings beating in China to yield the tornado in Oklahoma, order springing from disorder as shown by the Nobel prize winner Ilya Prigogine, mathematical unknowability (the last is surprising and possibly not in everyone's everyday experience).

To sum up, and this has been a long and exhausting effort, let me assert that religious faith can be attained by a variety of roads--the vision, the voice from above, or by rational "Top Down" endeavor.   As the quote at the beginning put it, some are born with faith, some achieve faith and some have faith thrust upon them.   And the faith we have in Jesus Christ is as well founded in terms of empirical evidence and inner knowledge  as the faith we as physicists have  in what science tells us about the world.

Saturday, September 28, 2013

Quantum mechanics and the Real Presence--What reality should we believe?

Tantum ergo Sacramentum                 Down in adoration falling
veneremur cernui;                                  Lo! The sacred Host we hail;
et antiquum documentum                     Lo! O'er ancient forms departing
novo cedat ritui;                                       newer rites of grace prevail;
praestet fides supplementum               faith for all defects supplying,
sensuum defectui                                      where the feeble sense fail.


A little over 20 years ago, shortly after I had decided to enter the Church, I was being catechized by a very learned and wise priest (this was before the days of RCIA classes).  As a physicist, I was struggling with the notion of trans-substantiation, that by the action of a priest a wafer could be changed into the body and blood of Our Lord.     Our  pastor first asked whether I believed in the resurrection;  I said I did, and he said if I could believe in that miracle, why not in another one?   He then told me that while one might occasionally have doubts or concerns about a particular Church teaching, one was, nevertheless, required to maintain any article of Dogma as being possible (Fr. McA--forgive the faulty memory of an old man for phrasing this less elegantly than you did.)   Several weeks after this discussion, my doubts about the Real Presence were wiped away: during a 40 Hours procession  the Monstrance was being carried in to the accompaniment of Tantum Ergo;  I remembered enough of my high school Latin to translate the verses as they were sung, and as "praestet fides supplementum sensuum defectui" rang out, my heart filled, tears filled my eyes, and I knew without a doubt that the little cracker in that beautiful monstrance contained the body and blood, divinity and humanity, of Jesus Christ.  Amazing Grace!

I was reminded that the Eucharist is a continuing miracle and a mystery, after reading an article by Alicia Colon about a recent eucharistic miracle in Argentina:  a consecrated host changed into human heart tissue, verified by witnesses and by pathological examination of the tissue and DNA (please go to the link for a more detailed account).    There have been other Eucharistic miracles (see the Real Presence website ) confirmed by the same rigorous process the Church uses to confirm miracles for canonization.     Since faith is at the root of our belief in the Real Presence, my point in this blog is not to use such miracles as evidence, but to understand (in the spirit of St. Anselm--"faith seeking understanding") what underlays the continuing miracle of transubstantiation,

In that spirit, to understand what faith had already confirmed, I delved into the works of St. Thomas Aquinas and later theologians, Edward Schillebeeckx and Karl Rahner.   (Dear reader:  please be patient--quantum mechanics will rear its ugly head later.)   To this philosophical novitiate, the concept of "substance" was murky;  on the other hand, the term "accidents"--the physical attributes of a thing, as apprehended by the senses either directly or via instrumentation--was clearly defined.  One could proceed all the way down to the properties--the "accidents"--of the sub-atomic constituents of the Host, quarks and all, and find they had not been altered by the act of Consecration.  Then what would be the substance of the Host, before and after Consecration?  It occurred to me that "substance" just told us what a thing is, no matter what its appearance seemed to be and that in the Consecration, transubstantiation corresponded to the change of the "real thing--substance" from bread to Jesus Christ. To illustrate this notion for religion classes I gave to Catholic prisoners (nothing like a captive audience!), I used the following example:  holding up a twenty dollar bill I asked the class if that bill was not issued by the government but by a counterfeiter with the same kinds of paper, ink, etc, would it still be a legitimate twenty?   And of course, they all answered no.  (I've come later to realize that this example comes dangerously close to the heretical notion of the Real Presence coming about through transignification--see the links above.)

How then does quantum mechanics relate to the Real Presence?   This question didn't enter my mind until I read a comment by Prof. Stephen Barr (a physicist whose opinions on science and the Catholic faith I greatly respect) refuting a Jesuit priest's contention that modern physics has made transubstantiation a meaningless notion.   As I interpret his article, Barr argued that what quantum mechanics told us about physical reality was irrelevant to the truth of transubstantiation (a metaphysical reality?):

"In short, one can explain the doctrine of transubstantiation and distinguish it from other beliefs about the Eucharist without any use of the Aristotelian apparatus. I don’t know what quantum mechanics has to do with any of this. If anything, quantum mechanics makes a straightforward connection between what appears empirically and what is “really there” more obscure than it was in Newtonian physics, and to that extent would make it easier rather than harder to affirm the doctrine."

Before exploring this implied distinction between the knowledge of reality from science and from philosophy/theology, I'd like do a brief horsies-and-duckies discourse on quantum mechanics. (See the reference below * for a more complete account.)  First, quantum mechanics is itself a mystery: as the great physicist Richard Feynman remarked, "I think I can safely say that nobody understands quantum mechanics."    The theory gives probabilities for alternative results of experiments, probabilities that are confirmed to a high degree of accuracy (much like actuarial results--one may not know when any given person may die, but one does know that among a large number of 70 year old men, a well-defined percentage will die in the coming year).   Even though quantum mechanics is deterministic in a statistical sense, this probabilistic character bothers many physicists: Einstein himself opposed the probabilistic interpretation of quantum mechanics, insisting that "God does not play dice with the universe".

Second, from the beginning of quantum mechanics, scientists have posited a connection between the conscious mind and the role of the observer in determining quantum mechanical outcomes in experiments.  As d'Espagnat puts it, "The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment."   The conscious mind of the observer plays a role in making a choice of experiments and what is to be observed.  One interpretation of quantum mechanics,  proposed by John Wheeler and Raymond Chiao,  has it that the observer creates reality by the act of choice in doing the experiment.   Since Chiao's  article on this in the collection of papers on the Vatican sponsored conference, "Quantum Mechanics--Scientific Perspectives on Divine Action (Vatican Observatory Publications, 2001) is hard to access on the internet, I'll quote from a Counterbalance review of the article:

"He (Chiao) supports a “neo-Berkeleyan” point of view in which the free choices of observers lead to nonlocal correlations of properties of quantum systems in time as well as in space, giving Berkeley’s dictum, esse est percipi, temporal as well as spatial significance. Theologically he uses this generalized Berkeleyan point of view to depict God as the Observer of the universe. Here God creates the universe as a whole (ex nihilo) and every event in time (creatio continua). The quantum nonseparability of the universe is suggestive of the New Testament’s view of the unity of creation."

So, where does this lead us in understanding how quantum mechanics explains the Real Presence of Jesus Christ in the Eucharist? I'm not sure. I reject those mystical interpretations of quantum mechanics exemplified in "What the Bleep" and other works entangling Eastern mysticism with quantum mechanics--whatever the truths of their insights into Buddhism or other Eastern religions, they have no clue as to what quantum mechanics is about. On the other hand, as the French physicist/philosopher Bernard d'Espagnat has suggested, there is a "veiled reality" underlaying the mysteries of quantum mechanics, a reality which suggests the existence of God. But because there is also a mystery in the Eucharist, it does not mean that this mystery, the Real Presence, is explained by a quantum mechanical veiled reality. It may be that the perceived, but yet unknown relation between consciousness and quantum mechanics is that which will enlighten us, tell us how the metaphysical reality of transubstantiation is totally confirmed in physical reality, a physical reality that the Patristic Fathers acknowledged but did not bother to explain. And, finally, as my wife put it: "Aquinas said that God is rational; what we don't understand is not because it's beyond reason, but beyond our rational capacity."

*The best reference for a lay person on the quantum mechanical mystery is a fine book by Rosenblum and Kuttner, "Quantum Enigma: Physics Encounters Consciousness".

Sunday, September 1, 2013

Let's Hear it for St. Augustine--a Theologian for Our Times

Happy those who feast on wisdom and savor her knowledge,
She will nourish and refresh them.”
Happy Those Who Feast on Wisdom, Hymn for the Office of Readings, 28th August.

Who is your favorite saint? Mine is St. Augustine (Hippo), whose feast day was last Wednesday, August the 28th . Rather than giving his biography and conversion story (which most of you reading this blog would already know), I thought it would be worthwhile to demonstrate how relevant for us today are his words, particularly those dealing with the philosophy and theology of Creation.

In Book 11 of “Confessions” Augustine considered how God (and Heaven and the Word) could be eternal and yet create the universe at an instant in time.
How, then, shall I respond to him who asks, 'What was God doing before he made heaven and earth?' I do not answer, as a certain one is reported to have done facetiously (shrugging off the force of the question). 'He was preparing hell,' he said, 'for those who pry too deep'. (Chapter XII, 14).
And further:
“ There was no time, therefore, when thou hadst not made anything, because thou hadst made time itself. (emphasis added) And there are no times that are coeternal with thee, because thou dost abide forever; but if times should abide, they would not be times.For what is time? Who can easily and briefly explain it? Who can even comprehend it in thought or put the answer into words? Yet is it not true that in conversation we refer to nothing more familiarly or knowingly than time? And surely we understand it when we speak of it; we understand it also when we hear another speak of it.What, then, is time? If no one asks me, I know what it is. If I wish to explain it to him who asks me, I do not know. Yet I say with confidence that I know that if nothing passed away, there would be no past time; and if nothing were still coming, there would be no future time; and if there were nothing at all, there would be no present time. (Chapter XIV, 17)
The last statement resonates with contemporary cosmology, that time began with the Big Bang—as general relativity would have it, the four-dimensional manifold of space-time began at the singularity of creation. And St. Augustine's perplexed wondering about the nature of time is altogether in accord with our present-day confusion. In physics, time is a parameter, t, and the fundamental laws of physics are symmetric under the operation t → -t (going back into the past is equivalent to going into the future.) On the other hand, we know that the real world is irreversible, that there is an arrow of time, entropy: the dropped egg does not spontaneously reassemble back into one's hand, the movie camera doesn't run backwards except in science-fiction. Great minds--Boltzmann, Poincare, Prigogine--have engaged this conundrum, but there is no universally accepted answer.

St. Augustine held that God created the universe from nothing. Two fundamental (and surprisingly modern) notions were introduced by Augustine: first, Creation was instantaneous (from the Old Testament teachings of Sirach, he argued that six days was a metaphorical device); second, not all animal forms were present initially at creation—for some, the potential or seed to develop later in a different form was given initially (justifying evolution and the descent of species?). He also stressed that one should not use Scripture to contradict what reason and experience ("Science") tells us about the world:
"Often a non-Christian knows something about the earth, the heavens, and the other parts of the world, about the motions and orbits of the stars and even their sizes and distances,... and this knowledge he holds with certainty from reason and experience. It is thus offensive and disgraceful for an unbeliever to hear a Christian talk nonsense about such things, claiming that what he is saying is based in Scripture. We should do all that we can to avoid such an embarrassing situation, lest the unbeliever see only ignorance in the Christian and laugh to scorn."(De Genesi ad litteram; the Literal Meaning of Genesis, an unfinished work.)
Below are quotes revealing how Augustine reveled in the beauty of God's Creation, presenting arguments for a Creator that to me are even more powerful than the evidence of the red shift and the microwave background radiation.
Look around; there are the heaven and the earth. They cry aloud that they were made, for they change and vary. Whatever there is that has not been made, and yet has being, has nothing in it that was not there before. This having something not already existent is what it means to be changed and varied. Heaven and earth thus speak plainly that they did not make themselves: 'We are, because we have been made; we did not exist before we came to be so that we could have made ourselves!' And the voice with which they speak is simply their visible presence. It was thou, O Lord, who madest these things. Thou art beautiful; thus they are beautiful. Thou art good, thus they are good. Thou art; thus they are. But they are not as beautiful, nor as good, nor as truly real as thou their Creator art. (emphasis added). Compared with thee, they are neither beautiful nor good, nor do they even exist. These things we know, thanks be to thee. Yet our knowledge is ignorance when it is compared with thy knowledge. (Confessions, Book 11, Chapter IV.)
Now may our God be our hope. He Who made all things is better than all things. He Who made all beautiful things is more beautiful than all of them. He Who made all mighty things is more mighty than all of them. He Who made all great things is greater than all of them. Learn to love the Creator in His Creatures and the maker in what He has made.” (Commentary on Psalm 39, 9)


Although the thrust of this blog has been on St. Augustine's insights into a Creating God, he also had much to say on prayer, grace, God's goodness in sending us his only begotten Son, Christ, salvation, and generally, how to live as a Christian. Many of these words of wisdom are collected in “Augustine Day by Day”, a small leather-bound book that I read every evening at bedtime (compiled by John E. Rotelle, OSA and published by Catholic Book Publishing Co, New York). I'll quote just two of these.

Do you wish to receive? Then give! Do you wish to be forgiven? Then forgive! This is just a brief summary, Hear Christ say in another place 'Forgive and you shall be forgiven'. Forgive, give. And you shall be given what you desire—eternal life.” (Sermon 64-5; May 1st).

Bad times! Troublesome times! This is what people are saying. Let our lives be good and the times will be good. For we make our own times. Such as we are, such are the times. What can we do? Maybe we cannot convert masses of people to a good life. But let the few who do hear live well. Let the few who live well endure the many who live badly.” (Sermon 30-8; July 4th).

St. Augustine died as the Vandals were sacking Hippo, at the fall of the Roman Empire. Will we be able to be as strong as he when the barbarians of the 21st century are trying to destroy Western civilization?

Monday, August 19, 2013

The Pearl of Great Price--Pascal's Wager Revisited* *

Again, the kingdom of heaven is like a merchant in search of fine pearls who, on finding one pearl of great value, sold all that he had and bought it.” (Matt 13:45,46, RSV).


Blaise Pascal, courtesy "Science Kids" ( )

Among the pile of  Pascal's papers that were to be the “Pensees” was found a proposition that has kept philosophers and theologians occupied for the last 350 years, Pascal's wager:  betting on God is the prudent option. (Notes, below, 1-8)   What new insights can one bring to this, then, after all this time?  I will try to understand the wager from a perspective of contemporary decision analysis, for which the wager was possibly the first instance, and also comment on what happens after one accepts the wager.

First, some background: it is important to keep in mind that although Pascal was a mathematician and physicist of the first order, he did not believe it was possible to show from reason alone that God exists (so much for Anselm and Aquinas!) :

“If there is a God, He is infinitely incomprehensible, since having neither parts nor limits, He has no affinity to us.  We are then incapable of knowing either what He is or if He is.”

On the other hand we can know God by faith:

“But by faith we know His existence;  in glory we shall know His nature.”

The last part of this quote shows the route Pascal wants us to follow: there is an afterlife, and its benefits are infinite.  This being so, the odds for following God are infinite; whatever one might lose in believing, even if there were no God, is finite, whereas that which one can gain from belief,  if there is a God, is infinite:

“But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite.”

Pascal spoke as a counselor of gamblers, for whom (with Fermat) he had developed the first quantitative version of probability analysis. It will be useful, before the wager is recast in a more quantitative format, to give some mundane examples.


In contemporary decision analysis one can proceed in two ways:

1) to examine possible gains and losses for various options, in the absence of known probabilities,  and to choose that option  which would correspond (psychologically or economically) to a preferred strategy:

2) to use known or estimated probabilities for various outcomes and to choose the option with the maximum expected value (see below).     Let's  first assume that  probabilities aren't known,  and see what considerations  might be involved in  choosing an option.   Here is the example:

Investing 10,000 units (dollars or ??) in
1) a savings account at 2% interest;
2) a conservative stock portfolio paying 6% in a good market, and losing 10% in a bad market;
3) a sure thing—an unreported diamond mine in Northern Scotland that your Uncle Angus has told you about—you'll double your investment.

The  table below summarizes the possible outcomes;  the columns represent “state of nature”, that is “good” outcome for a particular option and “bad” outcome ( a – sign means a loss), the rows, the different options.

If you're an optimist, you would of course choose the diamond mine.   If you are a pessimist or  risk-averse, you would choose the option with the least possible loss, the Savings Account (you would follow what is called the mini-max principle in decision analysis(9), choosing the option with minimum possible loss).

Now suppose Uncle Angus was right about the diamond mine—you'd berate yourself for not having invested in it.   This regret is quantified in a decision analysis scenario and used to justify a “mini-max regret” approach (10) for decision making.   For each state of nature (column) you subtract the best outcome to give a negative figure for “regret”.    You then list the worst (that is most negative) regret for each row (option) and choose that option with the least negative worst regret, as shown in the following table:

The option with with the least negative worst regret is the diamond mine, so if you were to follow a mini-max regret approach you would choose that option.  Clearly this is the restatement, in contemporary decision analytic terms, of Pascal's choice for belief, absent a known probability for the existence of God.     Put as a table one would have, symbolically:

There aren't numbers here, but clearly the value for belief in the existence of God (and the afterlife),  X, is much greater than Y (the loss -Y one sustains by belief) or Z (the gain of a possibly hedonistic life that one sustains by unbelief), so the minimum worst regret (least negative) is that for belief in God.

If probabilities for outcomes are known or can be estimated, another approach is to use expected values for each option and choose the option with the maximum expected value.   To get an expected value you multiply each outcome value by the probability for that outcome and sum these products for all the outcomes for a given option.

Pascal did not presume to give a probability for the existence of God and the afterlife.  However he relied on the infinite value of the outcome to give an infinite expected value—any number (however small as long as it's not zero) times infinity is infinity. And as long as the imputed loss is finite, the expected value will be infinite.   This assumption has raised the hackles of philosophers, and counterexamples—such as mixed strategies(2,10) and the “St. Petersburg Paradox”—have been proposed to show how the assumption of an infinite value outcome leads to problems.     In particular, suppose one follows the strategy of choosing the toss of a coin to decide  whether to believe.    The probability will be half that you will  choose to believe, so the expectation value will be infinite,  even though there will still be a probability of one-half  that you have chosen not to believe.    In my opinion these are valid objections, but they ignore the thrust of Pascal's argument, that the gain from belief is so large, that for any non-zero probability of an afterlife, the prudent person will believe.    The statement can be best  put in the forms of odds for the existence of God and an afterlife:

If the odds are greater than the possible loss to gain ratio, then  one should make the wager.    For example, if you believe that the odds for  Great Britain winning the World Cup are 2 to 3  and the bookmakers are giving 1 to 8 odds for Great Britain (win 8, lose 1),  you should bet for, and not against Great Britain.


Who are those who would not accept the wager?   According to Nicholas Rescher (1), the following:

1) the hard-core atheist (if you don't believe in God, you wouldn't believe in the possibility of an afterlife);

2) “the all-out hedonist” (Dr. Faustus?);

3) “the all-trusting disbeliever”, that is, one who believes everyone goes to heaven, that as in St. Teresa's prayer, Jesus will lead all souls to heaven, especially those most in need of his mercy;

4) “the radical skeptic” who disbelieves in all knowledge;

5) theists (e.g Buddhists, Hindus) who believe in God but have a different conception of the afterlife;

6) those who believe in an afterlife but in their evil, like Satan, would rather live in Hell than serve the Lord.

We emphasize again that the argument of Pascal's wager is addressed to the prudential man—the agnostic who believes in the possibility of an afterlife (and God)--and is willing to act so as to gain that reward, even in the midst of doubts.  Is belief then a matter of will?  The agnostic accepts the premise of the wager, but says

“ I am so made that I cannot believe. What, then, would you have me do?”

Pascal responds:

“Endeavor then to convince yourself, not by increase of proofs of God, but by the abatement of your passions.   You would like to attain faith and do not know the way;  you would like to cure yourself of unbelief, and ask the remedy for it...There are people... who are cured of an ill of which you would be cured.   Follow the way by which they began  by acting as if they believed, taking the holy water, having masses said, etc.”

Now can one “fake it until you make it” as Pascal suggests?  Or will the sacraments be ineffective, because the motive of the recipient is mercenary?  Which of the Catechism dicta are appropriate,

(1131)”The sacraments are efficacious signs of grace....They bear fruit in those who receive them WITH THE REQUIRED DISPOSITIONS.” (emphasis added)


(1128) “The sacrament is not wrought by the righteousness of either the celebrant or the recipient, BUT BY THE POWER OF GOD.”  (emphasis added).

The second suggests that if one prays for faith, then the “top-down” approach will work, starting from the head  and eventually through to the heart 15, or, as Pascal suggests:

“ each step you take on this road you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognize that you have wagered for something certain and infinite, for which you have given nothing.”
As a personal note, let me add that Pascal was right and I'll say more about this in a forthcoming blog, "Top Down to Jesus--Bypassing the Road to Damascus".

*This material has appeared, in somewhat different form, as a posting on the Magis Facebook site with a more detailed account of the probability analysis, and as an article in "FAITH" magazine


    1. Nicholas Rescher, Pascal's Wager—a study of practical reasoning in philosophical theology (Notre Dame: University of Notre Dame Press, 1985).
    2. A good summary on the web, with additional references (including other web sites) is given by Alan Hajek:
    3. Daniel Garber, What Happens after Pascal's Wager—living faith and rational belief (Milwaukee: Marquette University Press, 2009).
    4. Itzhtak Gilboa, Theory of Decision under Uncertainty (Cambridge: Cambridge University Press, 2009), pp. 38-40.
    5. Bas C. van Fraassen, Laws and Symmetry (Oxford: Clarendon Paperbacks, 1989), pp.52-53.
    6. James A. Connor, Pascal's Wager—the man who played dice with God (San Francisco: Harper and Collins, 2006).
    7. All quotations are from Blaise Pascal, Pensees W.E. Trotter (Mineola, NY: Dove Philosophical Classics, 2003), #233, pp. 65-69.
    8. Paul Bartha, “Taking stock of infinite value: Pascal's wager and relative utilities.” Synthese 154 (2007), 5-52.
    9. James O. Berger, Statistical Decision Theory and Bayesian Analysis (New York: Springer-Verlag, 1985) p.18
    10. ibid, pp. 377, 387.

Friday, August 2, 2013

The Theology of Water--Is Design Intelligent?

"The water that I shall give him will become in him a fountain of living water, welling up into eternal life. This is a new kind of water, a living, leaping water, welling up for those who are worthy. But why did Christ call the grace of the Spirit water? Because all things are dependent on water; plants and animals have their origin in water. Water comes down from heaven as rain, and although it is always the same in itself, it produces many different effects, one in the palm tree, another in the vine, and so on throughout the whole of creation. It does not come down, now as one thing, now as another, but while remaining essentially the same, it adapts itself to the needs of every creature that receives it."  
Quoted in the "Office of Readings" (Monday, Week 7 of Easter),  from a catechetical instruction by St. Cyril of Jerusalem.

Atomic structure of ice; O's represent oxygen atoms;
H's represent hydrogen atoms;  blue lines represent
chemical bonds;  red lines, hydrogen bonds.
The title of this post, "The Theology of Water", is taken from a short story by Hilbert Schenck in a collection of science-fiction stories with a religious theme, "Perpetual Light", which I read several months ago.   
In this story, after fruitless searches in the rest of the solar system, some middle-aged astronaut scientists explore Titan,  the largest moon of Saturn, to find life.     Titan is unique amongst solar system satellites in having an atmosphere, albeit a very cold one.
The scientists don't find life in any form, but they do find a strange type of water:  freezing and melting points much lower than "earth" water, but still with the unusual feature of solid water (ice) lighter than liquid at the freezing point, and with other differences in the thermodynamic properties.  The different properties are in fact those that would be suitable for life on this cold world, if life existed.   In testing the Titan water, the scientists turn it into earth-type water and realize that they are the life for which water is intended.

I dispute the essential scientific point of this story, that water at comparable temperatures and pressures would be different on Titan than on earth.    The properties of ice-- its relatively high melting point (compared to what one might expect doing a Periodic table comparison), it being lighter than liquid water--and the unusual thermodynamic properties of water can be  traced ultimately to fundamental bonding properties, specifically to the properties of the hydrogen bond  (see the illustration above), which in turn can be explained (in principle) by fundamental physics--quantum mechanics and electrostatics. 
Nevertheless, in telling the story, Schenck makes this important point: the properties of water  are tightly linked to the properties of the planet earth in order to provide an environment suitable for life (that is to say, carbon-based life as we know it).    Here are those properties (and I quote from the story--all temperatures are in degrees Centigrade--0 degrees Centigrade is the normal freezing point of water):
1)  liquid water has a maximum density at 4 degrees.   If it didn't (if the maximum density was at the freezing temperature), the cold water would sink to the bottom of the ocean and earth's  average surface temperature would be more than 20 degrees lower;
2) if the vapor pressure or the unusually high heat of vaporization of water is changed, either too much or not enough cloud would exist, which, in either case, would be a meteorological disaster;
3) if the density of ice is greater than that of liquid water at the freezing point (for most substances the density of the solid is greater than that of the melt), the ice would sink to the bottom of the oceans and the oceans would be perpetually frozen at the bottom, leading to massive winds at the surface;
4) if the high specific heat of liquid water is reduced, the temperature stabilizing effect of the ocean is lowered, and more storms and lower average temperature results;
5) the properties of water are optimized for the tilt of the earth's axis (23.5 degrees from the vertical)--if it were 0 degrees tilt, the temperature stabilizing effect would be too large, with complete cloud cover and ice-caps down to 40 degrees latitude
6) in the story, the properties of water are set for a mean earth temperature that is optimum for metabolism at 98.6 degrees Fahrenheit (and guess to what temperature that corresponds?)

Our biochemistry crucially involves the chemistry of water and hydrogen bonding.   The structure and reactions of proteins, enzymes, and DNA is critically dependent on hydrogen bonding, internally and to other biochemical molecules.    This blog isn't an appropriate context for even an abbreviated biochemistry lesson, but here are some web sites  about biochemistry and about the role of hydrogen bonding in DNA and proteins that will give some simple ideas to start.   

Biologists interested in alien life have considered biochemistries other than carbon-based/H2O.  (See the Wikipedia article on hypothetical types of biochemistry .)   Of these, one based on ammonia, NH3, seems most likely.    However the hydrogen bonds between ammonia molecules are only half as strong as those between water molecules.   Also, the temperature range for liquid ammonia is much lower than that for water, -78 to -33 degrees, so chemical reactions would proceed much more slowly, possibly too slowly for life-sustaining reactions.

So, the chemistry of hydrogen-bonding is one of those "finely-tuned" realities of nature that enable human life to exist.  We recall the Anthropic Principle, used to explain the fine-tuning of physical constants and cosmological facts (among which are the age of the universe and the unlikely existence of a large moon for our planet) that enables the existence of intelligent, carbon-based life.   I have not invoked the improbability of such fine-tuning, because probability, as a quantitative measure, is not properly applied to a single entity, and there is but one universe--we can know no other despite the speculations of metaphysical cosmologists.

How then do we justify the unlikelihood of such fine tuning, cosmological, physical and chemical?    And when I use the term unlikelihood, I'm not referring to the improbability of picking one white ball out of a bag of a zillion black balls.    Rather, I'm saying that we can think of all sorts of other universes, with different physical constants and laws, for which our type of life would not be possible.    Indeed, it is hard to imagine how any of the operative laws/constants might be nudged just a little bit and still allow for our kind of life.

Such fine tuning for hydrogen-bonding physics and chemistry should not, I believe, be tossed as another ingredient into the Intelligent Design" (ID) stew.     As I understand  ID, its principal tenet is opposing the Darwinian model for evolution (common descent).   Proponents of ID argue that gradual changes in form or biochemistry that might enhance survival (the cornerstone of the Darwinian survival-of-the-fittest program) are not sufficient to achieve the drastic differences in morphology and the "irreducible complexity" of various biochemical schemes.   

To my mind this is a "God of the gaps" type argument--to attribute that which we don't understand to specific divine intervention.   Moreover, a God who frames fundamental physics so that variety and complexity grows "naturally" from a unified beginning is much more to be admired and worshiped than a God who assembles, Leggo-like,  all the objects of a Young Earth (including evidence for a 4.5 billion year old earth and a 14 billion year old universe).    Paul Davies puts it very well:

“...the hypothesis of an intelligent designer applied to the laws of nature is far superior than the designer ...who violates the laws of nature from time to time by working miracles in evolutionary history. Design-by-laws is incomparably more intelligent than design-by-miracles.[emphasis added]”  (The Cosmic Jackpot: Why our universe is just right for life." p.200)
"Design-by-laws" (in Davies' felicitous phrase) is just how the anthropic principle can be interpreted.    Since a  full discussion of the anthropic principle would require a much lengthier blog, I'll defer that.   But I would like to end with one further comment.    This is a blog entitled "Reflections of a Catholic Scientist".    And, as a Catholic scientist, my God is much more than a creator, a demiurge who designed the universe engine and pressed the starter button.    My God is a Trinity,  a personal God, who intervenes from time to time in history, who sustains the laws of physics that make the universe-engine chug along, and who came to us in the person of His son, verified by historical revelation.    

Monday, April 15, 2013

God, Symmetry and Beauty in Science II: A Personal Perspective

“Now, may our God be our hope. He Who made all things is better than all things. He Who made all beautiful things is more beautiful than all of them. …Learn to love the Creator in His creature and the Maker in what He has made.“(St.Augustine of Hippo, Commentary on Psalm 39).
..and there is no doubt of the supreme mathematical beauty of Einstein’s general relativity.” (Roger Penrose,The Road to Reality).
The Einstein field equation, shown above in abbreviated form, is considered by most physicists to exemplify the most beautiful of all physical theories, that of general relativity.  What are the requirements for a beautiful theory and how do these manifest, as St. Augustine has it, the Creator’s handiwork? The beauty is displayed in the mathematics of the theory, in the equations that relate it to the world.  A first requirement is generality/profundity–the equation has to be the basis for understanding a very broad and deep range of phenomena–as Einstein said,
I want to know how God created this world. I am not interested in this or that phenomenon. I want to know His thoughts; the rest are details.“ (as quoted by A.Zee in “Fearful Symmetry”)
A second requirement is conciseness–what theoretical physicists would call elegance–Hemingway versus Faulkner or James. An equation that covers a page or so of symbols may be important and general, but it would not be beautiful. Much is summarized in the tensor notation of the general relativity field equations, but this beautiful form did not come easily.   It was not the result of sudden inspiration, unlike the lay view of how great science is done, but the result of eight years of dedicated effort, as Professor John Norton so well describes, in his discussion of Einstein’s notebooks: “General relativity was an achievement of creative imagination.”    
A page from Einstein's notebook on the formulation of general relativity--
see linke above to Prof. Norton's web-page
 There are other beautiful equations: Dirac’s equation combining quantum mechanics and special relativity, which led to the discovery of anti-matter and the theoretical basis for particle spin.    And it was Dirac who said “It is more important to have beauty in one’s equations than to have them  fit experiments”, a sentiment with which I am not entirely in agreement.
Dirac's Relativistic Equation for the Free Electron
In this connection, both the theory of general relativity and the Dirac equation have been confirmed experimentally.     General relativity was confirmed initially by the bending of light during a solar eclipse and by its quantitative explanation of the advance in the perhelion of the orbit of Mercury (as well as many other confirmatory experiments since then).
  The Dirac equation explained the existence of electron spin and predicted the existence of the positron (a positively charged electron), found experimentally some four years later. 

There is one other beautiful equation I want to mention, which in my opinion is as important as the two above: Boltzmann’s equation for entropy (S) in terms of thermodynamic probability (W), 

                                       S= k logarithm(W) 

(k is the Boltzmann constant).
Boltzmann's Tombstone;
the Equation  S= k logW
is at the top and the bust is of Boltzmann
This equation (engraved on his tombstone–see picture–and tattooed on my younger son’s arm) justifies the Second Law of Thermodynamics (the scientific version of Murphy’s Law: the universe is running down, no matter what 
                                           or, you can’t unscramble eggs without doing work), 
a physical law that, according to Einstein, will still be true many hundreds of years from now, even if all other theories are invalidated.
Given that mathematics and mathematical physics have elements of beauty, what does this have to do with God?    The notion that mathematical truths are Divine is ancient history, going back to Pythagoras and Plato in ancient Greece. Augustine,  and more recently  Cantor (19th Century), argued that infinity is a manifestation of God’s ineffability.   
Why is science is explained mathematically? Or, as the renowned mathematical physicist, Eugene Wigner, puts it in his article, whence The Unreasonable Effectiveness of Mathematics in the Natural Sciences"?  The question was, of course, answered some 500 years ago by Galileo: 
The laws of nature are written by the hand of God in the language of mathematics.”

We want to understand the world and to recognize, as Scripture declares, that God looked on His Creation and saw that it was good. When you see children playing with toy cars or other objects and arranging them neatly in a line, you see the first beginnings of a desire for order and sequence.
Mathematics has an intrinsic beauty that is not constructed by our minds, but is discovered by us.   
Nautilus shell pattern illustrating the Fibonacci Sequence
(from "Heritage Math", by Savannah Morrow)
In nature, the pattern of sunflower florets, the nautilus shell, the growth of tree limbs is governed by the 
Fibonacci sequence,0,1,1,2,3,5,8,13… The rectangles combined from all the squares of the Fibonacci sequence have sides that have the “Golden Ratio” (“Golden Mean”), which the Greeks appreciated as beautiful proportion.    

 I want to emphasize that the beauty of pleasing proportion comes from more than symmetry.  Symmetry can be an element of beauty, but it neither a necessary element nor always a sufficient element.    It is the apprehension of order, an order that appeals to our intellect, that is the core of beauty.    This appeal to intellect distinguishes beauty from that which is simply good, according to St. Thomas Aquinas:
The beautiful and the good are the same in the concrete existent (in subjecto), for they are based on the same thing, namely on the form.   For this reason the good is approvingly called the beautiful.  Yet, they differ in their intelligibility (ratione).  For the good appeals to the appetite; indeed, the good is what all desire.  So, it has the intelligible nature of an end, for appetite is sort of a motion toward a thing.   On the other hand, the beautiful appeals to the cognitive power:  for things that give pleasure when they are perceived (quae visa placent) are called beautiful. (emphasis added).   St. Thomas Aquinas,Summa Theologica
Aquinas also requires that which is beautiful be profound (he uses the term “large” or “big” but I think that can be construed as profound, as applied to beauty in science): “Beauty is found in a large body”.
I think Aquinas also shows the connection between Beauty and God in his Fourth Way, (the fourth of five ways of demonstrating the existence of God), which can be stated using the conclusion of the syllogism given in the link, “Thus, there is something that causes the being and goodness of every perfection in all things, and this is God.”
The "Big Trees" of Yosemite Park
(note the small size of the person
in the foreground.)
My own appreciation of the beauty of nature (I was too young and ignorant to realize the beauty of science) came as a teen-ager, going to the Griffith Park Planetarium in Los Angeles, and later, working one summer in the  Forest Service at Yosemite and seeing the Big Trees in their then unspoiled setting.
And all this became reinforced, later on when I became a Catholic (but more of that in a later blog) and saw that all of science was realized in Psalm 19a, “The Heavens declare the glory of God.”