Tuesday, February 11, 2014

A Lesson from Two Homilies: Don't Argue on the Internet.

From the Archdiocese of Dublin
Pope Francis Inauguration Homily
"Non in dialectica placuit Deo salvum facere populum suum" ("It is not by ar­guing that God chose to save His people"). St. Ambrose
"Fortunately, there have always been pastors who have understood more about theology than most professors.” Karl Barth

A recent  article in Crisis magazine by James Kalb reminded me of two homilies  I recently heard, and of the lesson I should have learned from these.   The homilies were given by two different priests, both foreign-born:  Fr. X, Vietnamese, one of the boat people who escaped the Communists at an early age; Fr. Y, Nigerian, a Dominican.   (Aren't we fortunate, as a missioned nation, that bread cast upon the waters has returned?)   The Crisis magazine article is about the futility of argumentation on the Internet, a conclusion with which I heartily concur.

As the quote and the title of this post suggest, argumentation is not the way to evangelize.   This was the lesson of the two homilies.   It's been a while since I heard them, so forgive me, Fr. X  and Fr. Y, if I don't recast them exactly as you spoke.    Fr. Y was discoursing on the Gospel, Matthew 10, in which Jesus sends the apostles out and tells them "And whosoever shall not receive you, nor hear your words, when ye depart out of that house or city, shake off the dust of your feet." (Matt 10:14)   In his homily Fr. Y said that one should not contest with those--family members, friends, ...--who dispute your faith.   You should state what you believe and show, by the example of your life, what your faith means to you.     Fr. X's homily took off from the moving paean on the great gift of love, in First Corinthians, "...If I have not love..".   Fr X said we have to love our enemies and those who contest with us, otherwise we are not Christians.   We cannot disparage them or wish ill for them.

All this I should try to achieve (but often fail to) in my responses to those contending on the internet.   If a Geocentrist, or a believer in the Young Earth refuses to debate honestly the scientific premises of their beliefs, I can do no more than point out where they might seek other opinions.  If an atheist refuses to read the books refuting Dawkins that I recommend--I cannot, as with giving my dog medicine, coat the pill with peanut butter and slip it into his mouth.  (One of our dogs was very adept at licking off the peanut butter and spitting out the pill.)   So, the only thing to do is to love these people (even if I don't like them) and pray for them.     Perhaps the Holy Spirit will imbue them with grace, as it did one fervent atheist,  Anthony Flew, who came to believe "There is a God".    And this is all I can hope and pray for.

Sunday, February 9, 2014

Counterfactuals vs Faith

The Empty Tomb, from petecabrerajr.com
I believe in Christianity as I believe that the sun has risen: not only because I see it, but because by it I see everything else.”  C.S. Lewis
"For by grace are ye saved through faith; and that not of yourselves: [it is] the gift of God:"  St. Paul, Eph 2:8
Several weeks ago Alan commented on my post, "Top-down to Jesus" , and caused me to think in depth about the intellectual component of my faith:
 "Hi Bob. Am I right in interpreting this as saying that the crux of your conversion process was becoming convinced by Morison that the resurrection was a real physical event of the type claimed by the Catholic Church and that no other possibility is consistent with the existence of the documents that came to be included in the New Testament of the Christian Bible? And if that is the case, would your faith be broken (eg) by the discovery of a document reliably dated to the time of the event which describes the empty tomb as resulting from removal of the body by some interested parties who claim to have relocated it to an as yet unexplored location where on subsequent investigation remains of the appropriate type and date are discovered?" 
Before responding fully to this comment, let me say that the crux of my conversion process was not only the account of the Resurrection in  Morison's Who Moved the Stone",  but the whole process that caused those in the Roman world to believe in a risen Jesus:

"What struck me even more on going from "Who Moved the Stone" to 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."

The comment of the Pharisee, Rabbi Gamaliel, quoted in the New Testament, is even more relevant:

"But a Pharisee named Gamaliel, a teacher of the law, who was honored by all the people, stood up in the Sanhedrin and ordered that the men be put outside for a little while. Then he addressed the Sanhedrin: 'Men of Israel, consider carefully what you intend to do to these men.  Some time ago Theudas appeared, claiming to be somebody, and about four hundred men rallied to him. He was killed, all his followers were dispersed, and it all came to nothing. After him, Judas the Galilean appeared in the days of the census and led a band of people in revolt. He too was killed, and all his followers were scattered. Therefore, in the present case I advise you: Leave these men alone! Let them go! For if their purpose or activity is of human origin, it will fail. But if it is from God, you will not be able to stop these men; you will only find yourselves fighting against God. (emphasis added)Acts 5:34-39.

Let me digress some more before responding directly to Alan.   I'm a science-fiction devotee, particularly of alternative history--what-might-have-been stories.   In one of these, "To the Promised Land" by Robert Silverberg, the Exodus failed, and so there was no  Israel, Judah and no Jesus Christ.  In another (the title and author of which I don't remember), Herodias sends a message to Pontius Pilate about the dream she had, and Pilate lets Jesus go free.   Jesus becomes an honored prophet, but there is no Christianity and eventually the Romans adopt Judaism as a state religion with the Emperor as head.   In another Constantine loses to Maxentius after crossing the Mylvian bridge, the small Christian sect withers away and Europe becomes a land of barbarians.    There are a host of other science-fiction stories (involving time travel and therefore less plausible) in which Jesus is either not crucified or someone takes His place.   These stories help us to understand the historical Jesus, but they are counterfactual--conceivable in an alternative, hypothetical universe but false in ours.

So, let's now examine Alan's comment as a logical proposition:
Premise 1:  A document is discovered leading to the relocation of the crucified body from the empty tomb to another location.
Premise 2:  This location is explored and "remains of an appropriate type and date" are discovered.
Conclusion:  Jesus was not resurrected.

Let's suppose, for the sake of argument, that both premises are true.   It would not follow that the discovered remains would be those of Jesus;  all that could be discovered by Carbon-14 dating, for example, would be that a young to middle aged male was buried at a time roughly corresponding to that of the Resurrection; there would be an error range overlapping by at least 20 years  the presumed date.  (Mathematical aside: one can show that the time error is proportional to the half-life of Carbon-14 times the error range in fractional loss of Carbon-14).  So this would not of itself be convincing evidence.  The controversial book The Jesus Family Tomb has evidence against it and for it, and again, does not provide proof that Jesus was not resurrected.   If you don't believe in the resurrection, it is convincing;  if you do believe in the Resurrection, it is not.   As with this book, I would discount whatever evidence there was for premises 1 and 2, against the most important intellectual support for faith in the Resurrection:   the spread of Christianity at a time when the civilized world was a particularly fertile field for such.   Could God have put his only Son on earth at any more favorable time?    And I believe the testimony in the New Testament--despite internal contradictions, there is too much there to be swept away by claims of mass hypnosis and all the other arguments that skeptics use to disprove the Resurrection.    Accordingly, I take Alan's proposition as a counterfactual--conceivable in an alternative (hypothetical) universe, but not possible in ours, but I thank him for giving an occasion for reflection.

I should add that faith is built on more than intellectual conviction.   I believe, with Pascal, that you can begin with rational choice to believe and eventually, faith of a deeper sort will follow, by God's grace.   In my case these moments have been aided by music, Pange Lingua during a processional of the monstrance, old hymns, Bach,  by quiet times at Adoration, by meditation during the Consecration and The Hours.

Finally, here's a relevant quote from St. Augustine:
"Faith is to believe what you do not see; the reward of this faith is to see what you believe." St. Augustine of Hippo, Sermones 4.1.1


Sunday, February 2, 2014

Do Quantum Entities Have Free Will? (And Do We?);
Or, "Does it Matter if God Plays Dice?"

"Of course I believe in free will. I have no choice."
 The Salon Interview, 1987, Isaac Balshevis Singer,  
"There is no evidence for determinism."
Princeton Lectures, John H. Conway
"Philosophy is too important to be left to philosophers" Unification beyond the Core , Frank Wilczek (also attributed to John Wheeler)

"Does it even matter if God plays dice?"
 Rachel Thomas' Plus-math Interview of John Conway
"...dearly beloved...be not disturbed by the obscurity of this question; I counsel you first to thank God for such things as you do understand; but for all which is beyond the reach of your mind, pray for understanding from the Lord, observing at the same time peace and love among yourselves...
"On Free Will and Grace , St. Augustine of Hippo

The Proof of the Kochen-Specker Theorem
(from plus-maths discussion, by Rachel Thomas)
In one of the later Foundation novels, Isaac Asimov envisages a world, Gaia, in which a super conscious mind pervades the world, from the smallest virus or rock to the humans (and robots) in it.   In such a world it would be natural that quantum entities have free will, and there would be nothing remarkable in the  Conway-Kochen Free Will Theorem :
"It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic – the universe’s response near the particle) is not determined by the entire previous history of the universe." The Strong Free Will Theorem, John Conway and Simon Kochen. 
I won't give an extended discussion of the proof (see the link in the caption for a very clear and detailed presentation by Rachel Thomas or the link for the quote for the rigorous mathematical proof).   Nor will I give an extended discussion of what free will might be (a topic about which philosophers have contended over the past millennia).   Halfway through writing this post, I discovered John Conway's six Princeton lectures on his Free Will Theorem online.   So really, rather than writing, I should just direct the reader to those lectures to see what the Free Will Theorem is all about.   I should also note that Conway does not claim his Free Will Theorem disproves determinism;  indeed, he says there is no way to disprove determinism, despite the fact that there is no evidence for it.

Nevertheless, I would like to use the Free Will Theorem (abbreviated as FWT) as a springboard to discuss several issues in interpreting quantum mechanics, namely how randomness and consciousness might enter into interpretations of quantum mechanics.  (Fear not, gentle reader--this will not be a "What the Bleep" presentation, or a jump into Eastern mysticism.)
From "The Spin Family"
5 sculptures by Adrian

First, let's see how the three axioms are empirically justified by contemporary physics;  I'll phrase the axioms to make the physics clear (I hope).
1.  SPIN.   There exist particles with intrinsic angular momentum (spin) with spin quantum number, S= 1, such that components of angular momentum along a preferred axis (as defined by, say, an electric/magnetic field or a polarizer) are 1,  0,  and -1 (for angular momentum, I'm using units of hbar, where hbar = Planck's constant/(2pi)).   The three components are shown in the illustration, "The Spin Family".   The total angular momentum vector precesses about the defined direction.   The upper cone shows the component with 1; the flat disc, the component with 0; the downward pointing cone, the component with -1.     Then quantum mechanics shows that the squared components of spin in some arbitrary choice of three perpendicular directions  must be either 0,1,1;   1,0,1; or 1,1,0 .   Note that photons have S=1, which is handy, because laser experiments can be done with photons.
2.  TWIN.   It is possible to produce a pair of particles with combined total spin angular momentum  0, in what is called a "singlet" state.    Thus, if particles a and b are so produced in a singlet state, then if particle a has angular momentum component (in units of hbar)  +1 along the defined direction, particle b must have component -1; if particle a has component 0, so must particle b;  if particle a has component -1, then particle b must have component +1.   If the two particles should be separated after being created in a singlet state, their spin components will still be correlated:  if a value of 1 or 0 for the squared component is measured in a certain direction for particle a, the same value must be measured in that direction for particle b.    This "entanglement" of spin components for separated particles was used by David Bohm in his version of the EPR (Einstein-Podolsky-Rosen) paradox and entered into Bell's Theorem, to confirm (or disprove) hidden-variable theories for quantum mechanics.   Such entanglement has been verified by many experiments (done to test Bell's  Theorem) over separated distances of many miles.
3. MIN (the original third axiom was FIN, having to do with limitations of speeds of transmission because of special relativity). We'll take two investigators A and B who are separated in space. The spin system A studies is labeled a, and the spin system B studies is labeled b; a and b are separated parts of a singlet, and each has spin quantum number S=1. Then Conway/Kochen state in axiom 3 that the choices by A and B for studying direction of spin components are independent:
"Assume that the experiments performed by two investigators A and B are space-like separated. Then experimenter B can freely choose any one of the 33 particular directions w, and a’s response is independent of this choice. Similarly and independently, A can freely choose any one of the 40 triples x, y, z, and b’s response is independent of that choice."
This axiom was chosen to make the FWT stronger, and to overcome objections made to the use of the FIN axiom.

We can proceed now with a short summary of the Conway-Kochen theorem proof.   First, it rests on the Kochen-Specker theorem (KST), which itself is quite important.   KST shows that hidden-variable theories for quantum mechanics having functional relations amongst the variables, independent of measurement procedures, are not valid.    Or, as Conway puts it, "the spin chooses its value on the fly." Accordingly, the  measured value does not depend on the previous history of the world.   Conway/Kochen's proof   assumes that separated investigators (A-Alice and B-Bob) have free will in choosing the direction for measuring spin.   Then by use of the Twin, Spin and Fin axioms, and the Kochen-Specker theorem, they show, in a proof by contradiction, that there is no functional relation for spin measurements by Bob, and therefore that the spin response is independent of the previous history of its worldline, i.e. the spin system's response is "free".

What do Conway/Kochen mean by "free will"?    Both for the investigator and for particle system they mean that the choice--what is done--does not depend on previous history.   A more conventional interpretation might be that free will is the ability to freely choose amongst several options.   The term "freely" is understood, but susceptible to a number of definitions. (As with Justice Potter Stewart's definition of pornography, "I know it when I see it").   In his Princeton lectures and interviews for Rachel Thomas,  Conway is quite emphatic that this freedom is not just "randomness".    To show how randomness might enter, he sets a backgammon tournament as an example.    The tournament director casts all the throws of the dice the night before the tournament, and then calls them out sequentially as each game is played, so that there is a level playing field for each contestant.  An example more familiar to me is that of a duplicate bridge  tournament.    At each table the four hands are dealt out randomly to begin with
Duplicate Bridge: Declarer's Hand  (Wikipedia article)
and the teams rotate from table to table, so that each team has played at each table with the same dealt hands.   There is a predetermined initial lay of the cards, but the players are free to deal with the sets of hands as they will.  (Is this an example of what philosophers call "compatibilism" in free will?)   Conway strongly argues that the FWT forbids randomness as an agency, whether occurring at the event or predetermined:
"That’s why it doesn’t matter if God plays dice with the Universe, or not. Even if we allowed random numbers into the Universe, which I’ll think of as God’s dice, that’s not sufficient to explain the lack of pre-determinism in quantum physics." quoted in Rachel Thomas's article.
I have a problem understanding this assertion.    Granted that the FWT  shows that the particle response cannot be predicted by a function involving past history, how exactly does that dispense with pseudo-randomness, predetermined before the world began?    What can we learn from physics, in general, and quantum mechanics, in particular, to understand Conway's argument?

Let's consider first "random noise" in electronic devices, my old friend from nmr spectroscopy and MRI.   Such noise can be characterized by mean square amplitude and correlation times, which in turn can be related to physical parameters.  Molecular motion candidates for randomness also obey functional relationships.  I've cited these as examples that don't contradict Conroy's argument about predetermined randomness.   Can the reader cite others that might?  I can't.

Schrodinger's Cat (U. Toronto, Physics)
If we turn to quantum mechanics, the state function, which most generally can be put as a superposition of basis states ("Schrodinger's Cat"), evolves deterministically.   The randomness comes at measurement, when the state function collapses, except for that basis state which gives the measured result.    Chance/randomness for the measured result comes from the component nature of basis states, and should be distinguished from weighting in a mixture of states.  (For links to basic web material on quantum mechanics, please refer to another post of mine, Quantum divine intervention.. )  Quantum Mechanics does not include this state function collapse on measurement as part of the general theory, and thus results the so-called Measurement Problem .

Amongst the various interpretations and alternative theories which attempt to resolve the measurement problem, I'd like to focus on two:  1) the relation between the observer, consciousness and measurement in quantum mechanics;  2)  many worlds/many minds (relative state theory).   From the earliest days of quantum mechanics, the great thinkers--Von Neumann, Wigner, Schrodinger--have posited that the final step in the measurement process was observation by a mind, a consciousness, and thus the mind and quantum mechanics were entwined.   The delayed choice experiment adds weight to this belief, I believe. There are many physicists (not abashed by the popularization of this notion in quantum leap science fiction) who subscribe to the Many Worlds interpretation of quantum mechanics that at each measurement one option is made apparent and the rest branch (into alternative universes, alternative minds?).

Here finally is my take:  as with John Wheeler, I believe there is a participatory universe created by the observer, conscious minds (ours? God's? both?).  The free will of the quantum entity is our own free will.    There is an infinitude of possible universes and our ego, our consciousness traverses these as it makes choices.   If there is a universe where we measure the particle going through one slit, there is another (with other conscious minds) where it goes through both. Such a view resolves a conflict between free will and God's omniscience and omnipotence--if God knows what our future actions will be, how can our will be free?  And the answer would be a type of Molinism, God is aware of all possible counterfactuals, but they are only counterfactuals for our mind, our ego, not for God.