Monday, October 26, 2015

Does Quantum Mechanics Speak to Catholic Teaching?

Schrodinger's Cat Images from light
 that never saw the object.  
Gabriela Lemos Nature article
"God is a mathematician of very high order and He used advanced mathematics in constructing the Universe. "  Paul A. M. Dirac, Nobel Prize Winner for his pioneering work in quantum theory. 
"Anyone who tells you they understand quantum mechanics is a liar." attributed to Richard Feynman (in one form or another), Nobel Prize winner for work in quantum electrodynamics.
"The one thing worse than a theology that attempts to draw connections between physics and God is a theology that believes it has no need of such connections, a theology that believes it can concoct the divine out of metaphysical whole cloth."  Philip Clayton, "Tracing the Lines" in Quantum Mechanics--Scientific Perspectives on Divine Action.*


On the right-hand column you'll see that of the five posts most visited on this blog, three deal with quantum mechanics and religion.  If, then, the relation between quantum mechanics and Catholic doctrine is intriguing, why not explore a general question:  does quantum mechanics inform theology, and if so, how?

What I will try to do is to put forth some general considerations.  Particular intersections of quantum mechanics with teachings of the Church are discussed in several posts on my blog (see the right hand column and References**).   Those who want to plunge into the deep end of the swimming pool,  might go to two volumes published by the Center for Theology and Natural Science (in collaboration with Vatican Observatory Publications).    The books are collections of papers presented at conferences called by Pope St. John Paul II to explore "Scientific Perspectives on Divine Action":   Quantum Mechanics,  Quantum Cosmology *.

I'll not try to give even a horsies and duckies sketch of the basics of quantum theory, except insofar as it is relevant to the theology discussed.    Also, I'm not going to discuss all intersections of quantum mechanics  and theology that might be of interest--some have already been covered in previous posts referenced below.


Quantum mechanics is peculiar (in more ways than one)!   The theory yields extremely accurate predictions and has not been proven incorrect in any experiments thus far.     Nevertheless (as per Feynman's quote) it is not intelligible in terms of every-day experience.    The mathematical formalism is elegant, and there is not a problem at the next stage:  letting physical quantities stand in for the mathematical variables.    The difficulty is at a higher level:  the interpretation of measurements in terms of qualitative models that correspond to our intuitive view of what the world is like.

If you go to the Wikipedia article on Interpretation of Quantum Mechanics you'll find 15 different interpretations (and there are subdivisions amongst many of these).   Some of these interpretations bear directly on matters of theology; others, not so much.      

Related to interpretation are general positions scientists and theologians take on just how quantum mechanics might be relevant to matters of faith.   Philip Clayton (Tracing the Lines*) has laid out five such positions:
  1. No reasons can be given, other than purely subjective ones, for any theological position (Cushing)
  2. Serious theological positions can be given in some cases, but quantum physics is too give rise to helpful theological conjectures (Polkinghorne).
  3. Some constructive theology can be written...even if our conjectures remain highly speculative (Chiao, Clayton, Russell, Stoeger, Tracy).
  4. ...Strong theological conclusions can be reached on the basis of modern physics (Dombs)... Intelligent Design theorists (Behe, Dembski) argue that evolution requires a prior intention and an in-built design on God's part.
  5. The convergence between the conclusions [of quantum physics] and the teachings of [Eastern] religious traditions is so great that they should no longer be regarded as separate realms...but as one integrated whole [Bohm, Capra].      
The names added in parentheses are those of physicists/philosophers/theologians who, according to Clayton, have taken the position in question.   My own position is between 3 and 4.    I'll consider below how three aspects of quantum theory--Superposition, Entanglement/Non-locality, the Measurement Problem--might bear on theological matters.

But before doing that, let me bring up one very general question about quantum physics that bears on theology.    Bernard d'Espagnat has suggested that quantum physics manifests a "veiled reality" .   If that is so, can this theory then tell us  what God is like, or would that also be "veiled", hidden?   Or, if God is not totally comprehensible to us--only partially intelligible--does that mean God and quantum mechanics are parallel mysteries?  Read the linked article and decide; but whichever way you decide, it is clear that quantum mechanics does inform theology in this matter.


In an early post  I speculated on whether the superposition principle of quantum mechanics might offer an analog of the Holy Trinity.    The general notion is that a state in quantum mechanics can be represents as the superposition of several component states;  one of the component states may be that which is detected by a measurement.    The notation used is conventional:  | "something", property> is a state that represents a "something" that has a "property".    So we write for God, the Trinity

        |God, the Trinity> = |God, the Father> + |God, the Son>  + |God, the Holy Spirit>

In that post, I explained how the act of measurement--picking out either God, the  Father,  God, the Son, or God, the Holy Spirit as the measured component state--might be envisioned:    for example, seeking God the Father in the prayer "Our Father";  seeking the God the Holy Spirit in looking within ourselves to be better, as in the Examen of the Night Prayer (Liturgy of the Hours).

In terms of the theological implications, this is but an analog, a way of trying to understand a deeper mystery,  much as the oft-used example of a triangle with God the Father, God the Son, and God the Holy Spirit at the corners of the triangle.  


Perhaps the most non-intuitive aspect involves the entanglement of two things, such that they seem to interact (instantaneously) even when physically separated at far distances from one another (the non-locality aspect).    There are many experiments that verify this.   The picture at the top of the column is one such:   photons (light particles) are experimentally prepared to be "entangled" and then physically separated by half-reflecting mirrors such that one passes through an object and another not.    Nevertheless there is an image from the photons that do not pass through or near the imaged object (the cat).

Here's a highly non-real example that illustrates entanglement.  I'm going to use the  conventional notation described above,  | something, property >   where the line and bracket indicate that "something" has some "property".    Let's consider a man, who votes Republican, state  |M,R>, and a woman, who votes Democratic, state |F,D>.     They get married and in the marriage vows promise to vote the same way.    So there results

|M,R> |F,D> (single)--->Marriage ---> |M,F,married> =|M,R>|F,R> + |M,D> |F,D>

Voting Republican or voting Democratic is entangled between husband and wife:
if the husband is away from home on election day and casts his absentee ballot as a Republican, his wife--even though she does not know how he has voted--will always vote Republican;   similarly, if the wife is away and casts an absentee ballot Democratic, the husband--without knowledge of his wife's vote--will always vote Democratic.    This is entanglement, action-at-a-distance.

The principle of special relativity, requiring that no information can be carried at a speed faster than light, is not violated (in real physics, if not the example), because no information is transmitted by the joint behavior of separated particles.

In the Divine Intervention Series on Quantum Mechanics*  Michael Redhead gives an exhaustive treatment of the assumptions--determinism, non-locality, etc--required for entanglement to hold.    In the linked article Redhead argues that entanglement and non-locality yield an "indeterministic", a "holistic non-separability" interpretation of quantum mechanics, such that
"[this interpretation] allows 'room' for divine action on particular occasions...Holism is an anti-reductionist thesis that shows how every element of the universe has for its ground of being the  totality of the whole, which pantheists would want to identify with God."
What are the theological implications of entanglement?   Eastern mystics hold that such entanglement shows that we are non-separable parts of a universe that is one entity and that the desired state is to immerse ourselves into that entity.

As a Catholic, I don't believe that claim.  In the Judaeo-Christian theology, God treats each of us as individuals, and when (or if) we attain heaven, we go as individuals.    Indeed, if one examines the entangled state function, each "something" remains as an individual, even though there is a necessary connection between its properties and the properties of the "something else" with which it is entangled.

The vision of entanglement is not a new one;  Dante foresaw it in the 14th century in The Divine Comedy:
"In its depths I saw in-gathered, and bound by Love into one volume, all things that are scattered through the universe, substance and accident and their relations, as if joined in such a manner that what I speak of is One simplicity of Light. I think I saw the universal form, of that bond, because, in saying it, I feel my heart leap, in greater intensity of joy."  Dante, Il Paradiso, Canto XXXIII, "The Final Vision""
One can also argue that entanglement justifies the relation between Jesus and us, as in the Parable of the King and the Final Judgment in Matthew:
 "Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
When saw we thee a stranger, and took thee in? or naked, and clothed thee?
Or when saw we thee sick, or in prison, and came unto thee?
And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me. [emphasis added]  Matthew 25:37-40 KJV


Quantum Mechanics is a beautiful theory, mathematically elegant, but there is a major flaw in its connection with the real world.   When the system has a state that is considered as a superposition of states, then a measurement will collapse that total state into one of the components.    To take our example above, the married state is a superposition of the state: man votes Republican, woman votes Republican,   and the other state: man votes Democratic, woman votes Democratic:
          |Married >   =  |M, R> |F,R>  +  |M,D> |F,D>   
The measurement (voting in an election) gives
        |Married> =  |M,R> |F,R>    or   |Married > =|M,D> |F,D> 
so the act of measurement (voting in an election) has "collapsed" the prior superposition to just one of the components.

The difficulty is that this "collapse" is not intrinsic to the basic equation used in quantum mechanics, the Schrodinger equation.   It can be added to the theory by use of a "Projection Operator" that represents measurement, but that is an ad hoc addition to the theory;  the ad hoc nature of this essential operator distresses many philosophers of science,  and some (not all) physicists. 

Two of the ways proposed to bypass the  Measurement Problem have theological implications.

Von Neumann proposed early in the development of quantum mechanics that the act of observation is a necessary (if implied) aspect of quantum theory, and, therefore it is this act of observation that induces the collapse of the state function;  since the choice to observe is controlled by a mind, it is the mind that executes the collapse and registers the final measured state.    The essential role of the observer' is confirmed in  experiments such as the delayed choice experiment.   This reasoning can be used to support a Berkeleyan view of reality, that reality is that which is perceived, "esse est percipi" (to be is to be perceived).   I've discussed this in a post, Quantum Divine Action via God, the Berkeleyan Observer, so please visit that post for an extended discussion.

In another answer to the Measurement Problem, the collapse of the  state function upon measurement is eliminated.   Instead of one state existing after measurement, all states continue to exist, either in alternate universes, or in alternate brain states.   This interpretation--the Many Worlds or Many Minds--is advocated by some physicists and philosophers, but rejected by others because of its "ontological extravagance".    There is a significant theological consequence for this interpretation that has to do with the Molinist view of God's Foreknowledge and Free Will.   For an extended discussion of this, I refer the reader to my post, "Free Will and God's Providence, Part IV".


Here, in brief, are the main ways in which quantum theory impinges on Catholic teaching and theology:
  • The "veiled reality" underlaying quantum mechanics strongly suggests that science, per se, can not reveal all that can be known of God.   
  • Entanglement makes a deterministic view of the world unlikely and allows freedom for Divine Action.  
  • The "Measurement Problem" yields two significant implications for Catholic theology:  one, a justification for a Berkeleyan view of reality, with God the "ultimate observer" maintaining the universe;   the other, a many worlds/many minds interpretation of quantum mechanics that fits in with a Molinist account of God's foreknowledge and free will.


*The linked reference to CTNS publications will show five icons for the books summarizing the Conference publications.   Click on the upper left (pink) "Quantum Mechanics" icon and a column will appear on the right hand listing each author's paper;   click on the author's name and a summary of his/her paper will appear.    Do similarly with the "Quantum Cosmology" icon.

**Listed below, in addition to those given in the post and in the right-hand column, are posts on quantum mechanics.  Links to web sites explaining quantum mechanics are given in the posts.    Enjoy!!
Philosophic Issues in Cosmology 3: Mathematical Metaphysics--Quantum mechanical models for early stages of the universe.
God, Symmetry and Beauty I:
 The Standard Model and the Higgs Boson.
God, Symmetry and Beauty in Science II: A Personal Perspective

Thursday, October 22, 2015

On Pope St. John Paul II's Feast Day:
His Rapprochement with Science

from Power Point Search, Sainted Word .  com
"Science can purify religion from error and superstition; religion can purify science from idolatry and false absolutes. Each can draw the other into a wider world, a world in which both can flourish."  St. John Paul II, Letter to Rev. George Coyne, S.J., Director of the Vatican Observatory.
 "Christianity possesses the source of its justification within itself  and does not expect science to constitute its primary apologetic." ibid.
"Faith and reason are like two wings on which the human spirit rises to the contemplation of truth; and God has placed in the human heart a desire to know the truth—in a word, to know himself—so that, by knowing and loving God, men and women may also come to the fullness of truth about themselves." St. John Paul II, Encyclical Fides et Ratio.
"It can be said, in fact, that research, by exploring the greatest and the smallest, contributes to the glory of God which is reflected in every part of the universe."
St. John Paul II, Address on the Jubilee of Scientists, 2000
NOTE:   This post was published in  June, 2014.   Today is Pope St. John Paul II's Feast Day and I thought it appropriate to post it again.

Among the many posts and articles on the canonization of St. John Paul II*, there have been few comments about his efforts to effect a rapprochement between the Church and science (notice the upper case and lack thereof).    The term "rapprochement" has been chosen with care: "an establishment or resumption of harmonious relations" (Oxford English Dictionary).   The term is applied to peace treaties after a state of war, and although the Catholic Church has not declared war on science, there are those scientists who do think there is such a war, and there are those advocates of scientism--that science explains all we need to know about the world--who have declared war on the Church.    These last ignore the founding contribution of the Church to the establishment of science (see Stacy Trasanco's Science was born of Christianity , and the contribution of Catholic Religious (Mendel, LeMaitre amongst many) to science in Fathers of Science.

There are three ways in which St. JP II tried to bring about this rapprochement:  1) redressing the Galileo Affair;  2) making the position of the Church on evolution clear and consistent with both dogma and science;  3) instituting conferences on how Divine Intervention might be manifested in several scientific disciplines.      The first two have been dealt with at some length in the blogosphere, so I'll treat those only briefly.   I'll focus on the third, which has been an invaluable resource for me in my discussions of science and religion.


As George Sim Johnston puts it in his book, The Galileo Affair
"The Galileo affair is the one stock argument used to show that science and Catholic dogma are antagonistic. While Galileo's eventual condemnation was certainly unjust a close look at the facts puts to rout almost every aspect of the reigning Galileo legend." George Sim Johnston
Summarizing his arguments, one can say that both Galileo and some Church officials were at fault, but it was a different time with different concerns--high officials in the Church, initially sympathetic to Galileo, were defending orthodoxy against the onslaught of the Reformation.    Galileo was condemned not for his advocacy of the Copernican theory per se, but for his advocacy that Scripture was to be interpreted loosely (even though the same had been done by St. Augustine).   And his science was wrong--circular orbits for the planets and his theory of tides.    All this is dealt with at greater length in the article linked above.

Nevertheless, this one piece of history has been the cannon used in the war of materialists and scientists against the Church, in their perceived conflict between the Church and Science.    In 1979  St. JP II asked the Pontifical Academy of Sciences to make an in-depth study of the affair.   Commenting on their report in 1992, he said, as an apology, explaining what had happened:
"Thanks to his intuition as a brilliant physicist and by relying on different arguments, Galileo, who practically invented the experimental method, understood why only the sun could function as the centre of the world, as it was then known, that is to say, as a planetary system. The error of the theologians of the time, when they maintained the centrality of the Earth, was to think that our understanding of the physical world's structure was, in some way, imposed by the literal sense of Sacred Scripture...."  St. John Paul II, Address to Pontifical Academy of Sciences, as quoted in  L'Osservatore Romano N. 44 (1264) - November 4, 1992 
Liberal news media made much of this apology, but it was only recognizing in a formal way earlier actions of the Church--removing Galileo's book from the index, setting up a Vatican Observatory--and setting the affair in a historical context.     What was important was his  affirmation in this apology that  science and the Church both have domains of truth, which do not deny each other--as in his address on evolution, "Truth cannot contradict Truth"


In his 1996 address to the Pontifical Academy of Science St. JP II, expanding on the doctrine set forth by Pope Pius XII in his encyclical Humani Generis, asserted that
"there is no conflict between evolution and the doctrine of the faith regarding man and his vocation, provided that we do not lose sight of certain fixed points."  St. John Paul II, 1996 address to the Pontifical Academy of Science.
Among these points is the most important requirement that the soul of man is endowed by God (the Holy Spirit) and not materially constructed:
"It is by virtue of his eternal soul that the whole person, including his body, possesses such great dignity. Pius XII underlined the essential point: if the origin of the human body comes through living matter which existed previously, the spiritual soul is created directly by God ("animas enim a Deo immediate creari catholica fides non retimere iubet"). (Humani Generis)" ibid.
He also showed much insight in commenting on the scientific aspects of evolution, that while evolution (the descent of species) is a fact, there is more than one theory--mechanism--proposed to explain evolution.
"As a result, the theories of evolution which, because of the philosophies which inspire them, regard the spirit either as emerging from the forces of living matter, or as a simple epiphenomenon of that matter, are incompatible with the truth about man. They are therefore unable to serve as the basis for the dignity of the human person."
It is unfortunate that both scientists and lay persons do not share St. JP II's understanding but equate the Darwinian model for evolution--"survival of the fittest"--with evolution, the descent of species.   And as with his apology for the Galileo affair, the liberal media made much of his acknowledgement that evolution is a fact, but neglected the historical and theological context which he brought to that statement.


In 1987 St. JP II instituted the first of a series of conferences, held at the Papal Summer Residence, Castelgandalfo, bringing together scientists, philosophers and theologians.    Not all of these were Catholic and, indeed, a few were not even theists, as the term is commonly understood.    He addressed the conferees at this first meeting ("Our Knowledge of God and Nature: Physics, Philosophy and Theology") via a letter to George Coyne, SJ, Director of the Vatican Observatory.  (I recommend the reader go to the link for that letter, to get the full import of St. JP II's thoughts on science and the Church.)  He stressed first, as in the quote at the beginning of this post, the contributions science could make to the Church and the Church to science, "Science can purify religion from error and superstition; religion can purify science from idolatry and false absolutes."  

He showed a sophisticated knowledge of frontier research in physics and biology in his comments on how scientists were trying to achieve a unified picture of scientific theory in physics and biology:
"The unity we perceive in creation on the basis of our faith in Jesus Christ as Lord of the universe...seems to be reflected and even reinforced in  what  contemporary science is revealing to us....Contemporary physics forms a striking example.  The quest for unification of all four fundamental physical forces--gravitation, electromagnetism, the strong and weak nuclear interactions--has met with increasing success....In the life sciences, too, something similar has happened.  Molecular biologists have probed the structure of living material...(and) have discovered that the same underlying constituents (genes and proteins coded by genes) serve in the make-up of all living organisms on earth." St. John Paul II, letter to George Coyne.
Although St. JPII argued that science and theology could, and should, mutually enrich the other, he did not think they should be unified, as in unified science or unified theology:
"By encouraging openness between the Church and the scientific communities, we are not envisioning a disciplinary unity between theology and science like that which exists within a given scientific field or within theology proper....The Church does not propose that science should become religion or religion science...To be more specific, both religion and science must preserve their autonomy and their distinctiveness....Christianity possesses the source of its justification within itself  and does not expect science to constitute its primary apologetic (emphasis added).   Science must bear witness to its own worth....neither ought to assume that it forms a necessary premise for the other."   ibid.
The quotation above reminds me of my encounters playing harmony parts (tenor and bass) in our Church instrumental group:  the musical lines are distinct, for the most part different,  but the harmony enriches the melody, as does science, theology.

Although St. JP II respected the integrity and distinctiveness of science and theology, he did emphasize that they could and should enrich each other in areas such as cosmology and molecular biology, and, accordingly, set up conferences to effect such enrichment.   He stressed the importance of putting scientific findings in a proper context, and the difficulty of doing such in our contemporary setting:
"For the truth of the matter is that the Church and the scientific community will inevitably interact....Christians will inevitably assimilate the prevailing ideas about the world, and these are inevitably shaped by science.  The only question is whether they will do this critically or unreflectively, with depth and nuance or with a shallowness that debases the Gospel and leaves us ashamed before history.   Scientists, like all human beings, will make decisions on what gives value and meaning to their lives and to their work.   This they will do well or poorly, with the reflective depth that theological wisdom can help them attain, or with an unconsidered absolutizing of their results beyond their reasonable and proper limits." ibid.
The last sentence in the above quote applies very well, I believe, to those cosmologists such as Stephen Hawking and cognitive scientists such as Stephen Pinker, who deny God on the basis of a limitless science.

I'll have to add that all the insights above (with the possible exception of the musical analogy) are those of  St. John Paul II.   I've been blessed in being able to bring these to the attention of others.

And, finally, as  a postscript, here is a list of these conferences and links to the proceedings published by the Vatican Observatory and University of Notre Dame Press.   On the web page of the Center for Natural Sciences and Theology that lists the books, you will see images of each book.  If you click on the book image, there will appear article headings at the right of the web-page, which will link to the article of interest.

Physics, Philosophy and Theology--A Quest for Common Understanding.
Quantum Cosmology and the Laws of Nature--Scientific Perspectives on Divine Action. 
Chaos and Complexity--Scientific Perspectives on Divine Action.
Neuroscience and the Person--Scientific Perspectives on Divine Action.
Evolutionary and Molecular Biology--Scientific Perspectives on Divine Action.
Quantum Mechanics--Scientific Perspectives on Divine Action.

*In what follows I will try to avoid the cumbersome form "Pope St. John Paul II", and meaning no disrespect (he is my hero!) will refer to him as St. JP II.

Friday, October 16, 2015

When was science born?
And guess what: the Catholic Church was the midwife.

Pierre Duhem (fromWikipedia)
"The history of science alone can keep the physicist from the mad ambitions of dogmatism as well as the despair of pyrrhonian scepticism. " Pierre Duhem, The Aim and Structure of Physical Theory


Some atheists and materialists would say that science arose in the 16th and 17th centuries, fully mature,  like Botticelli's Venus arising from the ocean.   According to them it arose then because Europe had shaken off the limiting bonds of Catholic doctrine.   Pierre Duhem's historical studies of science  shows that this is not so.*

Botticellis' "Venus arising from the ocean"


Rather, Duhem dates the birth of science as 1277, the year the Bishop of Paris, Etienne Tempier, condemned a number of errors from astrology and from the Peripatetic philosophers (those following Aristotle).    The condemned articles contended that the earth could not move, that worlds other than earth could not exist, that empty space (a vacuum) was impossible, and proposed principles of motion that were shown later to be false.

Bishop Tempier condemned the articles not because of scientific errors, but because they apparently limited God's power.   Once these Peripatetic dicta were declared non-binding, scholars--almost all of them clerics--were able to explore new ways to explain the world around us, ways that would grow into the scientific method.   Bertrand Russell's comment about the two books of Aristotle that embodied the condemned articles, "The Physics" and "On The Heavens" (which he greatly admired), is appropriate:  “there is hardly a sentence in either that is not contradicted by modern science”. 

Two areas of science. cosmology and dynamics (the physics of motion),  then grew from babyhood to adolescence in the period from 1277 to the 17th century. The growth in cosmology culminated in the Copernican Revolution, the idea that the earth was no longer the center of the universe but revolved around the sun.   But there was much work preliminary to that--the notion did not spring full-blown  to Copernicus.    I'll give a brief summary of Duhem's account of the development of dynamics below;  for a more complete discussion about this and the growth of cosmology please go to History of Physics before Einstein .

PHYSICS OF MOTION: 1277 To the 15th Century

The two Aristotelian principles of physical motion that were totally incorrect had to do with the effects of gravity and momentum--what kept moving bodies moving.   According to Aristotle, gravity manifested itself in the following ways:  heavy elements wanted to move to the center of the universe, the center of the  earth; the heavier the element (the more massive), the faster it would move;  lighter elements (air or fire) would move away from the center of the earth.  
Aristotle's theory of motion for projectiles was even stranger: 
"He held that the projectile was moved by the fluid medium, whether air or water,  through which it passed and this, by virtue of the vibration brought about in the fluid at the moment of throwing, and spread through it [the vibration through the medium]".  Pierre Duhem, History of Physics before Einstein, location 305
William of Occam (he of "Occam's Razor") argued against Aristotle's theory, as did other scholastics.   Jean Buridan (1295-1363), Rector of the University of Paris, gave  what is essentially the modern interpretation for projectile motion:
Buridan gave the name impetus [emphasis added] to the virtue or power communicated to the projectile by the hand or instrument throwing it; he declared that in any given body in motion this impetus was proportional to the velocity, and that in different bodies in motion propelled by the same velocity, the quantities of impetus were proportional to the mass or quantity of matter defined as it was afterward defined by Newton."  ibid, location 311
Thus "impetus" is that which we now term "momentum", defined by p = mv, where p is momentum, m is mass, and v is velocity.     The effects of air resistance and gravity (for a projectile thrown upwards) in slowing the motion, "destroying impetus", were taken into account by Buridan.   He thus analyzed the motion of the pendulum, the mechanism for impact and rebound, and the deformation of elastic bodies.

Albert of Saxony (1320-1390, Bishop of Halberstadt),  Buridan's pupil added on to Buridan's kinematic theory the following:
 "the velocity of a falling body must be proportional either to the time elapsed from the beginning of the fall or to the distance travelled during this time."  ibid, location 322.
This implies that gravity is a force that increases the impetus (momentum) of the falling body.     If these dynamic laws applied to motion of bodies on earth, they should also apply to the "heavenly" bodies, despite the restriction laid down by Aristotle that the motion of the heavenly spheres was governed by different laws than those of earthly bodies.   If there is nothing to reduce impetus--no air or medium to give rise to friction--then the heavenly bodies can keep moving without ceasing;  the initial impetus is given "by God at the moment of creation".    Thus the notion of inertia came into being.


Although Leonardo Da Vinci is better known for his art and work with  military armaments and flying machines, he did significant work in physics.    He understood the principle of conservation of energy and composition of forces in statics.   Although he recognized that the velocity of a freely-falling body is proportional to the time the body has fallen, he did not recognize the importance of increasing impetus due to gravity.

The significant law for falling bodies,  was proposed by Nicole Oresme (1320-1385, Bishop of Lisieux)
" a uniformly varied motion, the space traversed by the moving body is equal to that which it would traverse in a uniform motion whose duration would be that of the preceding motion, and whose velocity would be the same as that which affected the preceding motion at the mean instant of its duration."  ibid. location 571
Note that "uniformly varied motion" is equivalent to uniform acceleration. (These propositions were put forth before acceleration was understood as a property of motion.)  This means that the distance travelled in such motion during an interval of time would be that given by the average velocity for the interval (mean of beginning and ending velocity) multiplied by the time interval.

Oresme's proposition was modified by  Domingo Soto (1494-1560, professor of theology at Salamanca:
"The velocity of a falling body increases proportionally to the time of the fall.
The space traversed in a uniformly varied motion is the same as in a uniform motion occupying the same time, its velocity being the mean velocity of the former." ibid.
Soto's formulation leads to Galileo's  Law of Falling Bodies, that the distance fallen is proportion to the square of the time of fall.   This can be seen diagrammatically (as shown by Oresme) or algebraically** .

All the work described above sets the stage for Galileo--his important contribution was to introduce experimental tests of the mathematical hypotheses, inclined  plane experiments (done in my first year physics lab at Caltech), telescopic observations to confirm the Copernican hypothesis,   It should be noted that Galileo's ideas about dynamics did not yet reach the stage taught in first year physics classes today.
"He then taught that the motion of a freely falling body was uniformly accelerated; in favour of this law, he contented himself with appealing to its simplicity without considering the continual increase of impetus under the influence of gravity. Gravity creates, in equal periods, a new and uniform impetus which, added to that already acquired, causes the total impetus to increase in arithmetical progression according to the time occupied in the fall; hence the velocity of the falling body." ibid. location 970.
So we see that although Galileo achieved much, in different areas of physics and astronomy, he still followed in the tradition of his predecessors.   The relation of acceleration to force had to wait for Newton's Law, F= m a.


Why did this development of physics and cosmology occur begin and grow in Medieval Christendom, but not in the ancient Hellenistic worlds or other civilizations?    Excellent answers have been given, in some detail,  by Fr. Jaki and Dr. Trasancos in the references listed below, but I want to add my own opinion.   First, there was a world view, founded on Judaeo-Christian theology, that God was good and created a universe that was good and meant to be intelligible to mankind.   Second, as Duhem points out, the Medieval scholars were freed in 1277 from erroneous restrictions they would have had to follow if Aristotle's principles were to be a compulsory base for theories.    Third, in the earliest part of this growth they were priests;   this meant that they, as do academics today, had time to do scholarly work and did not have to worry about earning a living from non-scholarly pursuits.  

Finally, I want to emphasize again: there was a continuity of development from the 13th century to Galileo;  science did not spring full-blown with Galileo, despite his critical introduction of empirical verification of theoretical ideas and his insights in astronomy and dynamics.


*Duhem has written several histories of science.   The one linked above is the most easily (and cheaply) available.  Fr. Stanley Jaki has commented about Duhem's work and philosophy of science in several biographies, as has Dr. Stacy Trasancos in her book "Science was born of Christianity", which proceeds from Fr. Jaki's works.

**Consider the time t1=0 and time t2 =t (end of fall).   At t1=0, the initial velocity is 0.   At time t2, the velocity is v.   Soto's first proposition would say v = kt.
Soto's second proposition would give   d=v' t  where v' is the mean velocity =kt/2
(since v=0 at t=0).   Thus  d= (kt/2)xt = (k/2) t^2.     We now recognize the proportionality constant k as the acceleration, a.

Monday, October 12, 2015

Faith as a scientist; Faith as a Catholic

Est autem fides credere  quod nondum vides;
cujus fidei merces est videre quod credis
St. Augustine, Sermones 4.1.1
Illustration from Brainy Quotes.
"Anybody who has been seriously engaged in scientific work of any kind realizes that over the entrance to the gates of the temple of science are written the words: 'Ye must have faith.' It is a quality which the scientist cannot dispense with." Max Planck, Where is Science Going? p.24
  "Now faith is the substance of things hoped for, the evidence of things not seen."   Hebrews 11:1

"Science and religion are two windows through which we can look out at the world around us." Freeman Dyson, Infinity in All Directions


My recent post about Intelligent Design prescribed what science should and should not be.   To extend this discussion, I would argue that faith is required to do serious science (as the quote from Max Planck suggests); thus, contrary to what evangelical atheists say, faith is an attitude not restricted to the religious.

A useful preliminary to such a proposal would be a discussion about ways of knowing, what philosophers term epistemology.   We'll only do this briefly since this post is not a philosophy text.  For a more extensive coverage, please use the references listed below and the links.

One way of knowing is deduction, drawing conclusions from premises we believe to be true,  using logical procedures first set up by Aristotle--going from the general to the specific.  Here's an example (with apologies to Gelett Burgess), a "syllogism":
  • Major premise:   All cows are purple.
    From Seth Godin's web site.
  • Minor premise:   This animal is a cow.
  • Conclusion:         This animal is purple.
If you know the premises to be true, then the conclusion is true.    If the premises aren't true (as in this example), then the conclusion may or may not be true.   For example, you could paint a cow purple, or it could be a mutation.

Note the difference between the above and the following:
  • Major Premise:   All cows are purple.
  • Minor Premise:   This animal is purple.
  • Conclusion:         This animal is a cow.
The conclusion clearly need not follow; there might be purple animals other than cows (unless the premise were stated "Only cows are purple").   This type of false logic (fallacy), would be "affirming the consequent".

Induction is generally regarded as proceeding from particular instances or events to a general conclusion.   (I'm not referring in this context to the mathematical method of proof.)   Here's an example.   A bee-keeper notices that bees move up and down in a special way--"dance"--after they have been gathering nectar from a certain group of flowers.  The dance is the same for a given group of flowers.   The bee-keeper concludes that this bee-dancing is a communication to other bees about the location of the flowers and receives a Nobel Prize.  (We'll see below that science is generally more than collecting data and making inferences.)

Abduction is reasoning from a set of present facts to a possible explanation--events in the past that would account for the facts.   I've discussed this in my post on Intelligent Design, so I'll refer the readers to that discussion


Ask a scientist "what  is the scientific method?", and you're likely to get a blank stare or, "Am I on Candid Camera?" as a response.  If you ask a philosopher, you're may get any one of a number of answers, depending on whether the philosopher belongs to the "realist" or "anti-realist" camp.    There are philosophers who argue that there are no "laws of nature", but that scientific theories are models proposed only "to save the phenomena".  (See my post, Tipping the Sacred Cow of Science--Confessions of a Science Agnostic.)

I'm not going to expound on all the various philosophical schemes for how science works, but focus on one that I believe most closely corresponds to science as it's practiced.    I'll use a tree as a representation of how science proceeds, and do so with  a word diagram, rather than a picture since I'm not an artist:
  • SOIL:     The universe is orderly and intelligible.
  • ROOTS (specific assumptions about scientific principles):   Symmetry /  Conservation Principles; Uniformity (Cosmological) Principles;  The Second Law of Thermodynamics;  Microscopic Reversibility; replicability and predictability of observations.
  • TRUNK (The sap carried is methodology: measurement, observation, mathematics).
  • MAIN BRANCHES (divided into basic theories):  Quantum Mechanics; General and Special Relativity; "Classical" Electromagnetism; Classical Mechanics; Thermodynamics; Super-String Theory; etc.
  • SUBSIDIARY BRANCHES (e.g. for Quantum Mechanics): Quantum Electrodynamics; Laser Optics; Magnetic Resonance; The Standard Model; Molecular Structure; Solid State Theory; Super-conductivity;  etc...

As you'll note, sciences other than physics are neglected in this scheme--I could add chemistry, but I don't know enough about biology, geology, etc. to include them, so add on dear reader, if you're knowledgeable.

A few explanatory remarks are in order.   First, it is not a novel idea that faith in an orderly and intelligible universe is the soil in which the tree of science grows. A justification for this notion is that the enterprise of science grew in a Medieval Civilization, and only in this milieu; and that this civilization held the Judaeo-Christian premise that God ordered the universe to be meaningful--"The Heavens declare the glory of God" (Psalm 19a).   Pierre Duhem, Fr. Stanley Jaki and Dr. Stacy Trasancos have written about how science was born of Christianity, and not in other civilizations.    Although the works of science confirm the notion that the universe is orderly and intelligible, they do not prove it to be so;  that a scientist does believe it to be so is a matter of faith, and if he/she did not have that faith, why should he/she continue the exhausting effort of probing the mysteries of the universe?  Can anyone point out a great or even good scientist who did not believe this?

Second, the roots of the tree of science, its basic principles, are again matters of  faith.    They seem to be reasonable and confirmed empirically, but there is not logical justification for them--they are premises, not conclusions.    There is an equivalence between symmetry restrictions and physical laws, shown by Emmy Noether in the early 20th century:  for example, spherical symmetry yields conservation of angular momentum; symmetry under time reversal (t --> -t ) yields conservation of energy.    It's interesting that a symmetry thought before 1954 to hold universally, parity (mirror-image symmetry), was shown not to stand by itself, but to be incorporated into CPT symmetry (charge conjugation, parity and time reversal).

There are also esthetic judgments made about theories, judgments that are not considered here.   Such judgments are also articles of faith--that a theory that is "elegant" is to be preferred to one which is long and involved.    See my post God, Symmetry and Beauty in Science II for non-elegant thoughts on this.


The picture I'll give as the structure of my Catholic belief, a tree analog, will be unorthodox but, I hope, not heretical.   It will reflect my faith as it has developed during and since my conversion.**
  • SOIL:        The Trinity--God, the Father, above us; God, the Son, beside us; God, the Holy Spirit, within us.
  • ROOTS:    Dogma and Doctrine: The Incarnation, The Passion and Resurrection, the Immaculate Conception, The Eucharist & Transubstantiation, Apostolic Succession, the Primacy of Peter as Bishop of Rome; the Seven Sacraments, Scripture.
  • TRUNK:   The Church
  • BRANCHES:  Liturgy, Theology, Sacred Orders--religious and lay, the Sacraments in Parish Life, Missionary Life, Prayer and Devotion.
I'll admit that this representation is, perhaps, forced in order to make a comparison with the enterprise of science.    Nevertheless, there is a bedrock of faith, a soil--a belief in the Trinity Godhead--that nourishes my religious beliefs, and it is true that dogma and doctrine are the roots of my Catholic faith.    I invite the reader to draw his/her own tree of belief.

*Additional material on Deduction:

Charles Dodgson (better known as Lewis Carroll, author of the Alice books), an Oxford academic, gave us many amusing and complicated puzzles that mixed his love of nonsense and logic.   Some of Carroll's logical puzzles were exceedingly complicated, involving many statements and logical variables.   Notable among these is the "Pork Chop Problem", which has 15 statements and 11 logical variables.   The solution to such is not easy, and computer methods are helpful.   It may be difficult to make sure that none of the statements are contradictory, so that no paradoxes will occur.   To this end, there is a discipline,"satisfiability theory", in mathematical logic.

Can deductive logic always yield a unambiguous true or false set of  propositions?   In his very fine book, Labyrinths of Reason,  William Poundstone gives examples of logical paradoxes,  for which it is difficult to make a truth judgment.  Perhaps the most famous of these is the Cretan Liar paradox (see Star Trek, Fooling the Androids Episode):
"Epimenides the Cretan says, 'that all the Cretans are liars,' " Thomas Fowler, Elements of Deductive Logic.  Question: Is this statement true or false?
There is also the barber paradox, 
 "The barber is a man in town who shaves all those, and only those, men in town who do not shave themselves." Google search on Barber Paradox ... Question: Who shaves the barber?
Both paradoxes invoke self-reference, whence the paradox.    Bertrand Russell attempted to deal with the problem of self-reference by his "Theory of Types", which sets up a hierarchy of statements, i.e. statements about statements, statements about (statements about statements), etc.

**Other Posts on my Catholic faith.

The Pearl of Great Price--Pascal's Wager Revisited , Top-down to Jesus--On Bypassing the Road to Damascus, Are We Hard-Wired for Faith, God's Gift to Man--The Transforming Power of Music, Suffering: A Catholic| Jewish Perspective, among many others


Saturday, October 3, 2015

More St. Augustine:
Seek the Lord within, in silence

St. Augustine and the Fire of Wisdom
Here is some more good advice from St. Augustine, as given in Augustine Day by Day.

Seek the Lord Within. (October 2nd)
"Note the Psalmist's words: 'I sought the Lord and he answered me.'  Where does He reply? Within.  There you pray, there you are heard, and there you are made happy.
   Therefore, enter your heart.  Happy are those who enter their hearts and find no evil.  Commentary on Psalm 33.
Silence. ( October 3rd)

"Let us leave a little room for reflection, room too for silence.  Enter into yourself, and leave behind all noise and confusion.   Look within yourself.
   See whether there be  some delightful hidden place in your consciousness where you can be free of noise and argument, where you need not be carrying on your disputes and planning to have your own stubborn way.   Hear the word in quietness, that you may understand it."
 Sermon 52.

That's it...