Thursday, May 25, 2017

God the Creator and the "Useless Machine"

A Useless Machine, using a touch screen instead of a switch
External Finger:  "On" or "Box Open"
Internal Finger: "Off" or "Box Closed"
"No computer has ever been designed that is ever aware of what it's doing; but most of the time, we aren't either."  Marvin Minsky, Inventor of the Useless Machine.
"It from bit symbolizes the idea that every item of the physical world has at bottom — at a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe."  John Wheeler*


While surfing the internet, looking for my grandsons's birthday gift, I ran across the "Useless Machine," invented by the computer theorist, Marvin Minsky some 60 years ago.     A switch opens the lid on the box, and a hand comes out and flicks the switch to close it.    My version, using touch screens instead of a switch, is illustrated above.

The Useless Machine (also known as the "Leave Me Alone" machine) is one more item in John Wheeler's catalog of bits that make up "It".  The binary nature of computer instructions is given by:   "0" representing  "on" (or "open");  "1" representing "off" (or "close"). Thus the possible states of the box can be represented by (0,1),  as answers to the "yes/no" question cited in the quote from John Wheeler.

This picture is incomplete, I claim.   I will argue in this article that an important element is missing in the description of the Useless Machine, if we only list its algorithmic elements.


My own take on John Wheeler's arguments for "It from Bit" is given in another post, so I won't repeat that in detail here.   However, his premise of "Four No's"  is  relevant to this discussion, so I'll review these again:
  1. No "tower of turtles"**;
  2. No laws;
  3. No continuum;
  4. No space, no time.

The "no tower of turtles" statement asserts that infinite regress in a causal chain is not possible.  In this Wheeler, St. Thomas Aquinas, and other philosophers are in agreement.

The "no laws" assertion denies that the universe is a machine built on laws, a machine that would entail a multiverse, "universes in infinite variety and infinite number".    Rather, Wheeler envisions a "world self-synthesized":
"...the notes struck out on a piano by the observer-participants of all places and all times, bits though they are, in and by themselves constitute the great wide world of space and time and things." --John Wheeler,  Information, Physics, the Quantum: the Search for Links. p. 314
The "world self-synthesized" by "observer-participants of all places and all times"is Wheeler's "Participatory Universe", the notion that the universe is, as Bishop Berkeley suggested, created by observation: "esse est percipi".
Icon representing Wheeler's "Participatory Universe"
By looking backward in time (to distant galaxies) we create them
 But more questions are raised than answered here.  Would an annelid worm, an eagle, or a human synthesize the same world, or is it only "intelligent beings"?   If the last, what about the world synthesized by a Cro-Magnon man, an Australian aborigine, or Helen Keller?  There is not, as far as I can see, a coherent scheme here.  But I do have a different answer, given below.

By stating there is "no continuum", Wheeler denies the reality of transcendental and irrational numbers.   He uses quotes from the mathematician Hermann Weyl and the philosopher Willard Quine. to support that claim.  One should also note that  the "no continuum" condition requires that space and time must be discrete.

Wheeler's "no space, no time" condition is perhaps the most unappealing of these arguments. He claims that space and time are man-made inventions, and that at the beginning of the universe, "The Big Bang", quantum behavior would override General Relativity--there would be no connectivity in space, and before and after would have no meaning.


John Wheeler had an original and inventive mind.   In addition to "It from Bit" and the "Participatory Universe", he proposed a thought experiment, the Delayed Choice experiment, in which the choice of an experimenter, the observer, can yield a change in a  quantum trajectory even after the quantum entity has supposedly traversed its path.   Wheeler's idea has been realized experimentally by several physicists.  One of these, Raymond Chiao, has used the results to argue for a new interpretation of Bishop Berkeley's, "esse est percipi", "to be is to be observed":  God is the observer who creates and sustains the world by His act of observing it.

Which brings us now to the Useless Machine, and what it tells us, as a metaphor for the world,  about "It from Bit" and the Participatory Universe.    Here are three important things to note:

  • There is a finger external to the box that initiates the opening.
  • The machine did not build or design itself;  it was an external agent, Marvin Minsky, who invented it and an external agent, Claude Shannon, who had it built at Bell Labs.
  • The binary nature of the machine does not describe it completely--there is a lid, there is a finger inside the box, etc.   The states of the machine can be represented by 0 and 1, but we would need to know more than that to know all about the box, its attributes, its contents.

Can you translate these objections to taking the Useless Machine as a bit in "It from Bit" to taking the Universe as a collection of bits?   I can.   There is only one external finger, and that is the hand of God.    There is only one designer and creator, and that is the mind of God.   There is only one way to describe our world, and that is as God's Creation, sustained by Him, and only partially known by us.


*John Wheeler was one of the world's most creative and brilliant physicists.     See his NY Times obituary for a  partial list of his achievements.

**Wheeler is paraphrasing the expression "turtles all the way down".   There's  a famous anecdote about the elderly lady who  asserts that the earth is flat to a famous philosopher (two versions: William James or Bertrand Russell):  the earth rested on the back of a large elephant, which in turn rested on a larger turtle.   When asked what that turtle rested on, the lady replied, "don't be silly--it's turtles all the way down."

Wednesday, May 10, 2017

Suffering--Our Great Gift from God*

The Sufferings of Job, William Blake
from Wikimedia Commons
"In a sense, everything that happens to me is a gift from God.  I may resent disappointments, rebel against a series of misfortunes which I regard as unmerited punishment.   Yet in time I may come to understand that these can be considered gifts of enlightenment."
--One Day at a Time in Al-Anon, May 4
"The witnesses of the Cross and Resurrection of Christ have handed on to the Church and to mankind a specific Gospel of suffering. The Redeemer himself wrote this Gospel, above all by his own suffering accepted in love, so that man 'should not perish but have eternal life.' This suffering, together with the living word of his teaching, became a rich source for all those who shared in Jesus’ sufferings among the first generation of his disciples and confessors and among those who have come after them down the centuries"
--Pope St. John Paul II (Salvifici Doloris, VI:25).


Al-Anon is a Twelve Step group for family members and friends of alcoholics and addicts.  Some twenty-five years ago I went  regularly to Twelve Step group meetings for several years and then stopped because it seemed that I might get more meaningful support  from a deeper religious faith.  A "Higher Power" just didn't cut it then.   A month ago I  came back to Twelve Steps and started to attend a men's Al-Anon group, not because of family circumstances, but because I wanted support for self-examination and from group interactions that would complement and supplement my Catholic faith.

At a meeting two weeks ago a guy new to the group whose son had just hit bottom--been arrested with drugs, needles and other stuff--wondered why this had to happen to his family.  Another member brought up the quote given at the beginning of this post and there was then, shall we say, a  heated exchange of views.   I didn't participate,  but I did recall a talk given early on by a priest, recovering from alcoholism, in which he made the same point as the quote:  the alcoholic and his family have been given a gift from God, a gift that will enable them to grow in faith and spirituality.

I've been thinking about this problem since then.  It's one piece of the general problem of theodicy, why does God allow evil to exist.  As for myself, the suffering I endured 20 to 30 years ago did serve a good purpose:  it led me to my Catholic faith, after I had realized that belief in an amorphous "Higher Power" could not by itself sustain me.   What I will attempt to show in this post is how our Catholic faith does indeed show that suffering may serve purposes we do not perceive, and that we may transform that suffering into--not joy exactly--peace.


A common argument atheists use in attempting to disprove the existence of an all-good, all-powerful God, is that such a God would not allow the existence of suffering.    There are variations on this argument (one in Sean O'Carrol's recent apologetic for atheistic naturalism, "The Big Picture," relies on Bayesian probability analysis).   I'm not going to discuss such propositions in this post.   The counter-arguments to atheists have been given by better theologists and philosophers than I--see, for example, Professor Peter Kreeft's audiobook "Faith and Reason", and his CERC chapter, "Faith and Reason")

We, as Catholics, accept the dogmas and doctrines of the Magisterium,  and thus have a rational basis to understand (at least partially) why "bad things happen to good people".  As Catholics we must believe in Free Will and Original Sin, that Man is flawed, and that we inflict evil on ourselves.  We also believe, as in the parable of the rich man and Lazarus, that if bad things happen to us in this life, there is another life in heaven that will overshadow present misfortune.


There is a special Catholic perspective on suffering:  that by our own suffering we share Christ's salvific suffering for  us.   We should, therefore, not try to avoid suffering but to welcome it.   Quotes from the saints attest to this:

St. Augustine of Hippo:
"Trials and tribulations offer us a chance to make reparation for our past faults and sins. On such occasions the Lord comes to us like a physician to heal the wounds left by our sins. Tribulation is the divine medicine."
St. Francis of Assisi
"... our Lord Jesus, whose footsteps we ought to follow, called his betrayer “friend,” and offered himself willingly to his executioners. Therefore all those who unjustly inflict upon us tribulations, anguish, shame and injuries, sorrows and torments, martyrdom and death, are our friends whom we ought to love much, because we shall gain eternal life by those things which they make us suffer. And let us hate our body with its vices and sins, because by living in pleasures it wishes to rob us of the love of our Lord Jesus Christ and eternal life, and to lose itself with everything else in hell.” 

St. Ignatius of Loyola:
"If God sends you many sufferings, it is a sign that He has great plans for you and certainly wants to make you a saint."
"If God gives you an abundant harvest of trials, it is a sign of great holiness which He desires you to attain. Do you want to become a great saint? Ask God to send you many sufferings. The flame of Divine Love never rises higher than when fed with the wood of the Cross, which the infinite charity of the Savior used to finish His sacrifice. All the pleasures of the world are nothing compared with the sweetness found in the gall and vinegar offered to Jesus Christ." 
St. Teresa of Avila:
"Blessed be He, Who came into the world for no other purpose than to suffer."
"One must not think that a person who is suffering is not praying. He is offering up his sufferings to God, and many a time he is praying much
more truly than one who goes away by himself and meditates his head off, and, if he has squeezed out a few tears, thinks that is prayer."
St. John of the Cross: 
"Whenever anything disagreeable or displeasing happens to you, remember Christ crucified and be silent."
"The purest suffering bears and carries in its train the purest understanding."
St. Rafqua Al-Rayes:
"O Christ, I unite my sufferings to yours, my pains with your pains, as I look at your head crowned with thorns."
St. John Vianney:
 "Whether we will or not, we must suffer...There are two ways of suffering — to suffer with love, and to suffer without love. The saints suffered everything with joy, patience, and perseverance, because they loved. As for us, we suffer with anger, vexation, and weariness, because we do not love. If we loved God, we should love crosses, we should wish for them, we should take pleasure in them."
There are many more--just do a web-search: "quotes saints on suffering".


"Born of the mystery of Redemption in the Cross of Christ, the Church has to try to meet man in a special way on the path of his suffering. In this meeting man 'becomes the way for the Church', and this way is one of the most important ones."  Pope St. John Paul II, Salvifici Doloris.
In 1984 Pope St. John Paul II published his encyclical, Salvifici Doloris, three years after he had been shot by a would-be assassin.   Although I have not found any historical accounts to validate my conjecture that he suffered great pain during his recovery, it seems likely,  given that he had two sections of bowel removed.   It is reasonable to assume then that his Apostolic Letter was written in the context of his physical suffering, if not as a consequence of this suffering.

Pope St. John Paul II explores the dimensions of human suffering, from its relation in the Old Testament to God's Justice and the consequences of evil, the good man who suffers (Job), to the New Testament, in which Christ tells us to carry our cross and follow Him.   Pope St. John Paul II emphasizes that suffering is a mystery, but that by realizing  Christ suffered,  took on our sin and death, we can better understand God's purpose in allowing suffering.   By joining in suffering with Christ, we can unite our human distress with Christ's salvific suffering.   I do an injustice to the encyclical by this brief summary, and I urge the reader to read the letter in its entirety.    Two quotes are in order:
"In the Cross of Christ not only is the Redemption accomplished through suffering, but also human suffering itself has been redeemed,. Christ, - without any fault of his own - took on himself "the total evil of sin". The experience of this evil determined the incomparable extent of Christ's suffering, which became the price of the Redemption." Salvifici Dolores  18
 "Those who share in Christ's sufferings have before their eyes the Paschal Mystery of the Cross and Resurrection, in which Christ descends, in a first phase, to the ultimate limits of human weakness and impotence: indeed, he dies nailed to the Cross. But if at the same time in this weakness there is accomplished his lifting up, confirmed by the power of the Resurrection, then this means that the weaknesses of all human sufferings are capable of being infused with the same power of God manifested in Christ's Cross. In such a concept, to suffer means to become particularly susceptible, particularly open to the working of the salvific powers of God, offered to humanity in Christ. In him God has confirmed his desire to act especially through suffering, which is man's weakness and emptying of self, and he wishes to make his power known precisely in this weakness and emptying of self. " ibid. 23


It's a hard row to hoe, but I can only follow Catholic teaching.   When I pray the sorrowful Rosary and come to the fourth mystery, Jesus carries His cross, I pray that I can take on my sins, my failures, my suffering, offer them up and thereby  lighten the load of His cross.   We can not know what God wills for us,  but must assume that it is for our ultimate good.   And if we suffer now, we have to look to the parable of Lazarus and the rich man, to envisage that final reward that faith promises us.

*In an earlier post I have "discussed and compared" the Jewish and Catholic theologies of suffering;  see "Suffering--A Catholic | Jewish Perspective".

Saturday, April 29, 2017

Which is winning--scientism or religion?
I. What science is really all about

Albrecht Durer, St. Michael Fighting the Dragon
from Wikimedia Commons

“There is a fundamental difference between religion, which is based on authority, and science, which is based on observation and reason. Science will win because it works. [emphasis added] Stephen Hawking. ABC Interview, 2010"

The arrogance of scientists is evident nowhere more than in their zealotry against religion." Rabbi Yonason Goldson, Jewish World Review, 26th April, 2017.

"If we discuss a war between science and the Church (notice the difference in upper case), we must define what weapons are legitimate and where the battle is to take place." Robert Kurland,"Truth Cannot Contradict Truth"


This is to be the first in a series of posts about the supposed war between science--let me change that to "scientism"--and Catholic teaching.   I'll start off with some historical case studies to show how science has proceeded as a fallible human undertaking.  These case studies will then be set in the context of Imre Lakatos's  "Scientific Research Programme" to show how science works, its strengths and limitations.   Later posts will examine the arguments of evangelists for scientism and (I hope) rebut them.   But let's preface all that with a biographical note.

Reading about the recent "March for Science" and what it really stood for*,  I thought about my own past skirmishes between belief in science as the all-in-all and my need for a deeper faith.    I recalled that time 22 years ago when I told scientific colleagues--friends--about my conversion and Easter entry into the Catholic Church, and I imagined them shaking their heads and saying  "What's happened to old Bob, has he gone completely off his rocker?"  Those were the sort of comments I had heard 40 years earlier after a promising graduate student in theoretical chemistry became a Evangelical Christian and forsook his career.  

My friends were tolerant of my idiosyncratic behavior (to my face), but I could imagine them saying "he's not doing science any more so I guess this religion bit is an old age pastime."    Or maybe not.    According to them, belief in God indicated poor judgment, but not a moral defect.  It showed poor taste, like choosing Gershwin over Bach, a Buick over an Audi, or voting for Bush (41) instead of Clinton.

The toleration they showed is becoming is much less common nowadays.   There have have been a spate of recent books by theoretical physicists**, evangelical atheists who would  convert religious believers to their own faith, scientism.   What is scientism?  It's the belief that science can explain everything that needs to be explained and  that it can provide a foundation for morals and ethics.

That faith in science is misplaced.  As my favorite authority on the limits of science, Fr. Stanley Jaki, would put it:
"To answer the question 'To be or not to be?' we cannot turn to a science textbook."
--Fr. Stanley Jaki, The Limits of a Limitless Science.


Frankenstein's Laboratory, from Wikimedia Commons

My wife, a student of medieval history, has told me that "History tells you most of what you need to know about a subject", so we'll start with some examples from the history of science to show 1) that science is fallible and tentative, and 2) that it is totally dependent on empirical tests.

The Caloric Theory of Heat Refuted Experimentally
What is heat?  Nowadays we usually think of heat as a form of energy, but back in the 18th and early part of the 19th century that was not so.  At first it was thought that heat and combustion were inter-related via a hypothetical substance, phlogiston, but this theory was disproved by Lavoisier in the late 18th century by his experiments on oxygen and combustion. 

He then introduced a theory in which heat consisted of an invisible fluid, caloric, which flowed  from a hot thing to a cold thing.   The theory accounted quantitatively for temperature changes when a hot body was put into a contact with a cold one (e.g. dropping a given amount of cold water into  a given amount of hot water.)     A principle employed in such calculations was that since caloric was a substance, i.e. something material,  the total amount of caloric involved in heat transfer had to be conserved.
In 1798 Benjamin Thompson, Count Rumford, submitted a  paper to the Royal Society about his experiments in which boring a cannon could make water boil, and boring with a blunt instrument produced more heat than with a sharp one (more friction with the blunt).     The experiments showed that  repeated boring on the same cannon continued to produce heat, so clearly heat was not conserved.    This experiment validated another theory of heat, the kinetic theory, in which heat was due to the random motion of atoms and molecules.
However the kinetic theory, despite Rumford's groundbreaking experiment, still did not hold sway until some time after James Joule showed in 1845 that work could be quantitatively converted into heat.
James Joule: Work--->Heat
A diagram of Joule's apparatus is shown on the right:
Sir James Joule's Apparatus
from Wikimedia Commons
As the weight falls, the potential energy of the weight is converted into work done (a paddle stirs the water in the container against a frictional force due to water viscosity).   The temperature rise corresponding to a given fall of weights (work done) yields the amount of heat rise (in calories) of the known mass of water.   Since the temperature rise is very small, the measurements have to be very accurate.
It took 30 to 50 years after Joule's definitive experiment (and subsequent refinements and repetitions) for the kinetic theory of heat--heat caused by random, irregular motion of atoms and molecules--to be fully accepted by the scientific community.   James Clerk Maxwell published in 1871 a paper,  "Theory of Heat".  This comprehensive treatise and advances in thermodynamics convinced scientists  finally to accept that heat was a form of energy related to the kinetic energy of the atoms and molecules in a substance. 
Giving Birth to the Kurland-McGarvey Equation

I want also to illustrate how science works with an example from my own scientific career.  So as not to blow my own horn (too much!), I'm going to try to show not only where I succeeded, but where I erred.  A few years into my first academic position at Carnegie Tech (now Carnegie-Mellon University) a graduate student in my research group was facing a road block with his research problem.   A well-established theory was not giving results matching his data.  
After a lot of thought, it appeared  that we were not taking into account higher energy levels of the compound (potassium ferricyanide) he was studying.   Searching the library, I found a publication by Schwinger and Karplus (recalling my earlier graduate course in quantum mechanics) that offered a road to a solution.   After several weeks of intensive devotion, I wrote a paper that incorporated  density matrix techniques to account for contributions of all electronic levels and submitted it for a publication.   One reviewer pointed out a serious deficiency--I had neglected to account for mixing of excited states with ground state.  I acknowledged he was right, asked him to co-author the paper with me and we collaboratively worked it up for publication.  
There is an equation stemming from that work, (Google "Kurland-McGarvey Equation") that is widely enough used in the specialty that it doesn't need footnoting for reference.    So, one more small brick in the scientific edifice.
Now, the point of all this is to show that science proceeds  by correcting errors in theories,  errors in which theories--which are meant to be descriptive, not prescriptive--don't fit experimental data.    The refereeing process fifty years ago was one where authors were usually willing to be criticized and the reviewers of papers almost always tried to insure that the science in a published paper was good.   
Other Experimental Tests of Significant Theories
There are many more examples of theories that were confirmed--i.e. not falsified--by empirical results.  Links are given below to some examples of such experimental tests  in various fields of science.  
Each of these examples above can be rationalized in terms of Imre Lakatos' "Scientific Research Programme", which is discussed below.

Lakatos's "Scientific Research Programme"

The  "Scientific Research Programme" devised by Imre Lakatos can be thought of as a sphere:  there is an inner core of fundamental principles--not theories, but principles to which theories have to adhere; these principles are assumed, because they seem obvious and confirmed generally by our experience.   But, as we'll see below, there are  occasions when these fundamental principles are modified or violated.    Surrounding this core of fundamental principles is a shell of fundamental or primary theories (e.g. thermodynamics, general relativity, quantum mechanics).   Surrounding this shell of fundamental theories are other shells representing auxiliary theories derived from the primary theories and other auxiliary theories.  MRI, chemical bonding, heat transfer are examples of  such auxiliary theories.  And finally  there is an outer shell of experimental facts or data.   The interplay between the shells and core that shows how science works is illustrated below.
Lakatos "Scientific Research Programme
In this diagram the inner core principles are linked to fundamental and auxiliary theories, as shown by the black arrows.   There is feedback from data to theories,  as shown by the red arrows.   There is even feedback from data and fundamental theories to inner core principles, as shown by the red arrows.
Examples: Rumford, Joule
The core principle involved in the caloric theory of heat was the conservation of caloric (since it was a substance).  Count Rumford's cannon-boring experiments showed that the more the cannon was bored, the more heat was produced;  therefore the supply of heat in the cannon was inexhaustible and clearly not conserved. 
A core principle involved in Joule's experiment is the First Law of Thermodynamics:  conservation of energy, with heat and work as forms of energy.   Note that this conservation principle is linked to a fundamental theory of thermodynamics developed in the middle of the 19th century  and to theories of classical mechanics developed in the 18th century and early 19th century.
Examples: Einstein's Relativity theories
Einstein's two theories of relativity are  striking examples of how theory influences  fundamental principle (the red arrow), or perhaps more accurately, how fundamental principles are proposed as a basis for general theories.  His theory, special relativity, introduced the following new general principles:

  • the laws of physics are the same for systems ("frames of reference") moving at constant velocity (i.e. "inertial systems");
  • the speed of light (in vacuum) is constant, regardless of the speed of source or receiver;
  • neither energy nor mass is conserved but only mass + energy (from E=mc²)

His general relativity theory introduced the "equivalence principle", that inertial and gravitational mass are the same.   In every-day terms, this principle says that a person (mass m) in an elevator accelerating upward experiences a force holding him to the floor due to earth's gravitation, mg, plus a force due to the acceleration of the elevator, ma.   This is the same force that the person would experience on a planet where the gravitational acceleration would correspond  to g+a, or in a spaceship accelerating at a rate g+a
Example: The Ultra-violet Catastrophe and Quantum Theory
At the end of the 19th century classical physics came across a real stumbling block.   Theory predicted that the energy of a "black body" (a body radiating energy, in thermal equilibrium with its surroundings) should go to infinity as the wavelength of the radiated energy approached zero (toward the ultra-violet end of the electromagnetic spectrum).
Planck resolved this problem by positing that energy was not transferred continuously, but only in a small discrete packet which he called a quantum of energy.  (And thus was born quantum mechanics.)   So this is another example of how data, experiments affect fundamental principles.
Example: Parity Conserved? Right- and Left-handed Symmetry
Parity refers to mirror symmetry.  For example,  many organic molecules are 
Chiral Amino Acids--Right and Left-handed
from Wikimedia Commons
either right- or left-handed  (see the illustration at right of two amino acids, constituents of proteins:  COOH is the organic acid group, NH2 is an amino group, C is the central carbon, R represents a general group attached to the carbon). Now biological molecules can be chiral either as a whole, or with respect to the constituent parts.   For example, amino acids found in nature are left-handed;  sugars found in nature are right-handed;  DNA as a whole has a right-handed spiral (helix).    The question of why only one kind of handedness for biological molecules came about has fascinated chemists and biologists since the time of Pasteur 150 years ago.  There are recent theories to explain this, but they are to some extent conjectural.
Conservation of parity (handedness) had been a fundamental principle of physics  until the late 1950's, when a proposal to test it for nuclear weak force interactions--e,g, beta decay of Co-60 nuclei--showed that it was violated.  (See here for an expanded story.)   Since that time a conservation principle, CPT symmetry, linking parity (P) with charge (C) and time reversal (T) has been found to hold.
In all the examples described above there is an interaction between theory and experimental data: either the data confirms the predictions of theory or the data requires a theory  to be modified or discarded.    These interactions are nicely summarized by the Lakatos model, "The Scientific Research Programme".


How do we go from “how science works” to “what science can’t do”? The most comprehensive scheme and, to my mind, the one that best matches actual scientific practice is that of Imre Lakatos, described above. Note again these elements of the scheme: a network of hypotheses AND experimental data. The combination of theory and data requires that predictions or explanations made by models and theory must be validated empirically, if the theory or model is to be truly part of science. Measurements must be replicable, which is to say that essentially the same results are required, for whichever team does the measurement or performs the experiment.
Fr. Stanley Jaki has put more stringent requirements on science:
" synonymous with measurements, which are accurate because they can be expressed in numbers. Those numbers relate to tangible or material things, or rather to their spatial extensions or correlations with one another in a given moment or as time goes on. "The Limits of a Limitless Science," Asbury Theological Journal 54 (1999), p.24
This need for numerical assessment strikes out disciplines which most people would regard as science—biology, geology, paleontology, and such. Here I would have to disagree with Fr. Jaki: abduction and retroduction can be used to assess non-numerical data rigorously. A fine example is the development of the tectonic plate theory. It started in 1915 with the continental drift hypothesis of Alfred Wegener, based on the matching coastline shapes of western Africa and Eastern South America, and the striking similarity of strata and fossils on the two coasts. In the 1960’s seismographic data showed that continents and ocean floors rested on vast tectonic plates which were vehicles for continental drift. So, both qualitative and quantitative evidence entered into validation of the theory.
A much more important limit to science has been set by Fr. Jaki:
 "Hamlet's question, ‘to be or not to be,’ has a meaning even deeper than whether an act is moral or immoral. That deeper meaning is not merely whether there is a life after death. The deepest perspective opened up by that question is reflection on existence in general. In raising the question, ‘to be or not to be,’ one conveys one's ability to ponder existence itself. In fact every bit of knowledge begins with the registering of something that exists. To know is to register existence. But this is precisely what science cannot do, simply because existence as such cannot be measured.[emphasis added].”--Fr. Stanley Jaki, loc. Cit., p.30.
What this means is that science can not explain itself. Science can not show why it gives us a partial picture of the world expressed mathematically, or to use the Nobel Laureate Eugene Wigner’s apt phrase, science can not explain “the unreasonable effectiveness of mathematics” by an underlying scientific theory. The only justification for this success is empirical—it works!
Therefore science can not answer questions about religion. It cannot neither prove nor disprove the existence of a Godhead, nor the existence of the Trinity. Thus, to say that science “proves” the existence of God, is as much an error as saying it disproves that God exists. We can only say that all that we learn about our world from science is in accord with that world which an omniscient and omnipotent God would create.

*See  the linked column by Rabbi Goldson and blog posts by William (Matt) Briggs (Statistician to the Stars)
**I'm thinking of Stephen Hawking, Lawrence Kraus, and most recently, Sean Carroll.   I'll be reviewing Carroll's book, "The Big Picture", in another post. It's the best of the lot. 

About Me

My photo

Retired, cranky, old physicist.   Convert to Catholicism in 1995.   Trying to show that there is no contradiction between what science tells us about the world and our Catholic faith.   Intermittent blogs and adult education classes to achieve this end (see   and

Extraordinary Minister of Communion volunteer to federal prison and hospital; lector, EOMC.
Sometime player of bass clarinet, alto clarinet, clarinet, bass, tenor bowed psaltery for parish instrumental group and local folk group.

And, finally, my motivation:
“It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking.
Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.”
St. Augustine of Hippo, The Trinity I,8.