topics: |  philosophy | religion | history | science

Review

Keith Ward discusses some of the conflicts between religion (Christianity)
and science (he teaches divinity at Gresham College London).  Writing
cogently and readably, he shows how many stalwarts of modern science were
profoundly religious - his epynomous Pascal, and especially, Newton.

For many of us who grow up finding Newton in every textbook, it does not
seem that he would need to invoke God in his physics.  He was of course, one
of the most brilliant scientists ever.  He integrated scattered pieces of
ill-formulated knowledge previously known into the laws for motion and
gravitation and made significant advances to calculus to apply them to
terrestrial and cosmic problems.  

Newton is in other words, an icon of determinism - the idea that things in
the world can be predicted from an initial state based on a set of laws. 

Newton's recourse to God in mechanics

However, it turns out that Newton himself was no determinist.  

Every science has its unexplained phenomena, and in Newton's work, he met
this when he considered the mutual forces in the moon-earth-sun system.

In December 1590, a lunar eclipse predicted by Tycho Brahe started earlier by
more than an hour.  In his subsequent investigations, he found that at
times of syzygy (new or full moon), the sidereal velocity of the Moon
(against the background of stars) was faster than expected. On the other
hand, when it is in a phase perpendicular to the sun-earth line, its velocity
was slower than expected.

Newton was able to resolve Tycho's observations in the Principia.  However,
he calls his solution “imperfect” (Preface to the first edition).

Proposition 66 of Book 1 of the "Principia" states: 

	Prop. 66: Let three bodies mutually attract each other under an
	inverse-square law, with the two lesser ones (E) and (M) revolving
	about the greatest one, (S). Then if the greatest body (S) is moved
	by this action, the smaller inner body (M) will describe about the
	larger inner body (E), by radii drawn to it, areas more nearly
	proportional to the times, and a figure more closely resembling an
	ellipse, than would be the case if the greatest body were not
	attracted by the smaller ones, or were at rest.

This proposition is followed by 22 corollaries that describe the
perturbations of M caused by S, purely in prose, without giving the
calculations.  Newton was considering the gravitational perturbations due to
the third body as a sequence of impulses, equally spaced in time, which
instantaneously alters the velocity of M.  The results tally well with the
Variation (Astronomy) observed by Tycho Brahe. 


The process involves solving for the motions xM, xE, xS, from three
coupled non-linear differential equations for the three bodies :

	xM-dot-dot = Gforce due to mE + Gforce due to mS
	xE-dot-dot = Gforce due to mS + Gforce due to mM
	xS-dot-dot = Gforce due to mM + Gforce due to mE

where Gforce is the gravitational force (inverse-square law), and m are the
masses. 

This is known as the three-body problem, and is hard to do analytically.
In Book 3 of the Principia, Propositions 25 to 35, Newton obtiains an
approximate solution.  

The three-body problem

It is known now (since the 1890s) that no general solution could be found.
In fact, the problem has become one of the classic "difficult" problems in
classical mechanics.  Some key steps in the history of this problem are:

* Lagrange in 1772, extending work by Euler, presented a constant-pattern
      	solution, based on a set of five points in the plane of E's
      	orbit around S, called the Lagrangian points L1 to L5.


  The medium mass E is orbiting about the heavier mass S.  Objects close to E
  exhibit nearly elliptic motion (e.g. moon), whereas objects orbiting the
  heaviest mass S are affected by E and can have "horseshoe" orbits in the
  S-E frame (e.g. the 150m asteroid 54509 YORP).  Other objects that are
  close to the L3/L4 may have "tadpole" orbits, (e.g. the 300 m asteroid
  2010 TK7)

* In 1888, Heinrich Bruns showed that certain perturbations of the Lagrange 
	patterns can lead to divergence. a few years later, Poincare
	generalized this to show that a general solution to the 3-body
	problem cannot be obtained algebraically, though specific classes of
	motions are possible under certain conditions.

* In 1911, William MacMillan found a special solution, later extended by K A
  Sitnikov (1961).  The system is one where the larger masses are equal and
  orbit in a plane, while the smallest mass moves in a plane perpendicular to
  these.

* In 2013, 13 new classes of solutions
	were presented by Milovan Šuvakov and Veljko Dmitrašinović of Belgrade. 


	Solutions to the three-body problem, such as the "figure eight" and
	"yarn," can be viewed on an abstract shape-sphere (top) or in real
	space (bottom).  image from sciencemag.org

Newton's approach

Thus, though he didn't know it, Newton was up against a tough problem. 
Nonetheless, he was able to get a working solution for the Sun-Moon-Earth
system, which explained present observations adequately. 

However, when he considered a system with more bodies (Jupiter, Mars,
Saturn, etc.) each of these interactions would be affected when any pair
would approach close.  His pen and paper formulations were inadequate to
the task, and he appeared to have concluded that the planets should long
ago have either fallen into the Sun or flown off into outer space.

Yet the solar system appeared to be stable. So Newton concludes in Principia,
that God must occasionally step in to fix the system: 

	The six primary Planets are revolv'd about the Sun, in circles
	concentric with the Sun, and with motions directed towards the same
	parts, and almost in the same plane. . . . But it is not to be
	conceived that mere mechanical causes could give birth to so many
	regular motions. . . . This most beautiful System of the Sun,
	Planets, and Comets, could only proceed from the counsel and dominion
	of an intelligent and powerful Being.


Is this recourse to a "God of the gaps" indicative of a form of
egocentricism?   Is it saying that "our theory is infallible", so there must
be a divine explanation? 

The recourse to God is based on the assumption that our ideas and
calculations can't be wrong - and the only explanation left must be that a
God is fixing it.  In the case of Newton, of course, he had a strong belief
in divine powers and the occult, but still this is the only point where he
invokes God in mechanics, so we must wonder about it...

Recourse to God

Newton is such a hero of science, that the fact that the very idea that he
may have suggested that God comes in from time to time to set the planets
in order seems preposterous. 

Today similar recourses to religion are taken by many when encountering a
phenomenon that science has not been able to solve, so far.  

The challenge to religion started with the outside world, but after Darwin,
new challenges emerged re: the origins of man in the sphere of evolution.
However, the attempt to re-cast religion in the light of present scientific
theories raises questions about the fundamental validity of the God theory
that has to be reformulated keeping some kind of a core notion intact while
giving up on some of the contradictions. - AM

Excerpts

God was declared dead in 1883 by Friedrich Nietzsche.  God may have been
killed by many things, but a major suspect was science. 1

In many traditional relig views, human beings are the most important things
in the universe, and the whole of nature is created to serve humans.
After Galileo, that view was turned completely on its head.

The legend has grown up that Galileo was the first and decisive battle
between science and religion.  Galileo certainly won the battle, so some
popular histories of sci depict the story as the beginning of the death of
God and the triumph of materialism.  8

Copernicus, Polish catholic: On the revelations of the heavenly spheres,
1543, the year of his death.  dedicated to Pope Paul III, carrying an
endorsement by the local cardinal.  Little public reaction.

Heliocentrism is heretical: Galileo

However, in 1616, [60 years later] consultants to the Congregation of the
Holy Office [the Inquisition] declared that the heliocentric hypothesis was
formally heretical.

When Galileo later re-affirmed the Copernican hypothesis in a very combative
way, an affronted scientific establishment took action.  G was convicted in
1633 and placed under house arrest, where he remained till his death nine
years later.

The conflict however, was not so much between Christian faith and the
Copernican view that the earth circles the sun, as between established
Aristotelian science and the 'new science' of close observation and
experiment that was threatening the old scientific elite. 9

The Catholic Church assoc itself firmly with the authority of Aristotle, who
was taken to be mastere of all sci (except theology, where he needed to be
corrected by Thomas Aquinas, the 'angelic doctor').  Aristotle's concepts of
substance and accident, form and matter, act and potency had been used in
framing doctrines like that of transubstantiation and ideas of God.  His
system of the four types of causality: material, formal, efficient, and
final, was accepted as the proper framework for natural science. 9

Note: Aristotle himself was a major revision of the Bible - Archbishop of
Paris prohibited Aristotle in the 13th c. 10

TRANSUBSTANTIATION: the Roman Catholic doctrine that the whole substance of
	the bread and the wine changes into the substance of the body and
	blood of Christ when consecrated in the Eucharist

see also: Douglas Adams on Gallileo and the Vatican
		what the Vatican said to Gallileo was, "We don't dispute your
		readings, we just dispute the explanation you put on
		them. It's all very well for you to say that the planets sort
		of do that as they go round and it is as if we were a planet
		and those planets were all going round the sun; it's alright
		to say it's as if that were happening, but you're not allowed
		to say that's what is happening, because we have a total
		lockhold on universal truth and also it simply strains our
		personal credulity".

Reconciling with science

One move to reconcile science is to say that statements in the Bible are not
literal, but metaphorical.  The Church has long been used to interpreting
Biblical statements abt God metaphorically.  God does not literally "trample
on the nations" (Habakkuk 3:12).  ... Saying that the universe was created in
six days, for instance, had usually been taken metaphorically. 11

Cardinal Bellarmine, writing in 1616 to Galileo's friend Foscarini, saw this
possibility:

	I say that if a real proof be found that the sun is fixed and does not
	revolve around the earth, but the earth around the sun, then it will
	be necessary, very carefully, to proceed to the explanation of
	passages of Scripture which appear to be contrary, and we should
	rather say that we have misunderstood these than pronounce that to be
	false which is demonstrated. 11

Humans removed from centre of the universe

Aquinas: everything in creation ultimately existed 'for the sake of man' 13

Are we the only form of "intelligent life" in the universe?  If so, Though
phys not in centre, we may still be the most "advanced" species, so we still
remain at the center of God's love.

As the physicist Enrico Fermi asked, "Why aren't the aliens here?"
Since some stars are billions of years old, some other intelligent forms may
have evolved elsewhere long before us... 14

* Martin Rees: Our cosmic habitat, Princeton U Press, 2001 15

Far future:  In a std picture of the very far future, the universe wd be a
dilute and ever-diminishing soup of extremely low-energy photons, neutrinos,
and gravitons moving virtually freely thru a slowly expanding space.  15

Modern sci seems to sugg that the existence of humans is a freakish
accident. 17

But probab of humans, based on the God premise, is higher than that based on
the sci premise. 18

Was it really worth billions of years of cosmic evolution just to produce
Lalu Yadav?  19 [(orig.) was Tony Blair]

Biggest objection to God: why "bad" things happen?   This is why some
scientists will accept the existence of a super-intelligence, but remain
sceptical abt whether it is good or benevolent. 20

The intellectual beauty of being

Newtonian revolution was to see nature as the intelligible product of one
rational and elegant cosmic mind.  This later gave rise to the idea of nature
as an impersonal machine, whose laws are absolute, fixed, and
all-explaining. For N however, the laws of nature demonstrate the presence
and power of one supreme God of immense wisdom, intelligence, and spiritual
purpose.  For N, science is a spiritual enterprise, seeking greater
understanding of the wisdom of God. 24

2.3. Kant: Freedom and Determinism

Influenced by Newton, believed that all events have a suff and determining
cause, i.e., given its antecedent physical state and the laws of nature, each
event happens by necessity; there is no alternative to it, and it has to be
just what it is. [LAW OF PHYSICAL DETERMINISM]

Then how can there be moral freedom / autonomy?  Kant himself was forced into
the desperate expedient of saying that I am morally free ion the noumenal
world (the world of things as they really are, which I can never know by the
senses or by obsvn), whereas I am wholly determined in the phenomenal world
(the world of the senses and of physical science). 28

Many philosophers are, like Kant, 'compatibilists' -- they think we must
believe in both physical determinism as well as freewill. 29

Ridley, Matt, Genome 1999: There is no such thing as evolutionary
progress... The black-smoker bacterium [that inhabits sulphurous vents in the
Atlantic seabed] is arguably more highly evolved than the bank clerk (p.25)

Kant felt that to be morally responsible, I must be able to do what is right
or not do it.  Nothing must determine my choice between those alternative
paths except my own decision.  While my decision can be influenced by many
factors, I am free to do something not determined_ by any past event or law
of nature.  [RADICAL FREEDOM: action undetermined by any prior physical
cause.] 29

Kant: people were responsible even for the places and circs in which they
were born.  Once born, they were determined by laws - but they had freely
chosen the circs of their birth. 29

Newton's "God hypothesis"

Newton himself did not believe in determinism.  He believed that God would
have to act in the universe at rare intervals to keep the planets in stable
orbits around the sun.  Otherwise, they would after a very long period of
time fall out of their orbits into the sun.   It is this hypothesis that
Laplace referred to when he is alleged to have told Napoleon: I have no need
of that hypothesis.

Laplace had refined the Newtonian calculus so that more precisely
formulated equations of motion could dispense with the need for divine
intervention.  Thereby he got rid of what the Cambridge mathematician
A.C. Coulson called the "God of the gaps" [Coulson: Science and Christian
Belief, 1958]
It was partially Laplace's success in showing that such a God was not needed
that gave impetus to the hypothesis of physical determinism. 30

Aside: Neil deGrasse Tyson on Newton's God Hypothesis

The Perimeter of Ignorance :
A boundary where scientists face a choice: invoke a deity or continue the quest for knowledge
From Natural History magazine, Nov 2005

    Newton's law of gravity enables you to calculate the force of attraction
    between any two objects. If you introduce a third object, then each one
    attracts the other two, and the orbits they trace become much harder to
    compute. Add another object, and another, and another, and soon you have the
    planets in our solar system. Earth and the Sun pull on each other, but
    Jupiter also pulls on Earth, Saturn pulls on Earth, Mars pulls on Earth,
    Jupiter pulls on Saturn, Saturn pulls on Mars, and on and on.

    Newton feared that all this pulling would render the orbits in the solar
    system unstable. His equations indicated that the planets should long ago
    have either fallen into the Sun or flown the coop — leaving the Sun, in either
    case, devoid of planets. Yet the solar system, as well as the larger cosmos,
    appeared to be the very model of order and durability. So Newton, in his
    greatest work, the Principia, concludes that God must occasionally step in
    and make things right:

       The six primary Planets are revolv'd about the Sun, in circles concentric
       with the Sun, and with motions directed towards the same parts, and almost
       in the same plane. . . . But it is not to be conceived that mere
       mechanical causes could give birth to so many regular motions. . . . This
       most beautiful System of the Sun, Planets, and Comets, could only proceed
       from the counsel and dominion of an intelligent and powerful Being.
       And lest the systems of the fixed Stars should, by their gravity, fall
       on each other mutually, he hath placed those Systems at immense
       distances from one another.
	        [Principia, General Scholium, end of Book 3. p.1157 in Hawking,
      	 [hawking-2003-on-shoulders-of|Shoulder of Giants, also, wikisource.]

    In the Principia, Newton distinguishes between hypotheses and experimental
    philosophy, and declares, "Hypotheses, whether metaphysical or physical,
    whether of occult qualities or mechanical, have no place in experimental
    philosophy." What he wants is data, "inferr'd from the phenomena." But in the
    absence of data, at the border between what he could explain and what he
    could only honor — the causes he could identify and those he could not—
    Newton rapturously invokes God:

       Eternal and Infinite, Omnipotent and Omniscient; . . . he governs all
       things, and knows all things that are or can be done. . . . We know him
       only by his most wise and excellent contrivances of things, and final
       causes; we admire him for his perfections; but we reverence and adore him
       on account of his dominion.

    A century later, the French astronomer and mathematician Pierre-Simon de
    Laplace confronted Newton's dilemma of unstable orbits head-on. Rather than
    view the mysterious stability of the solar system as the unknowable work of
    God, Laplace declared it a scientific challenge. In his multipart
    masterpiece, Mecanique Celeste, the first volume of which appeared in 1798,
    Laplace demonstrates that the solar system is stable over periods of time
    longer than Newton could predict. To do so, Laplace pioneered a new kind of
    mathematics called perturbation theory, which enabled him to examine the
    cumulative effects of many small forces. 

    According to an oft-repeated but probably embellished account, when
    Laplace gave a copy of Mecanique Celeste to his physics-literate
    friend Napoleon Bonaparte, Napoleon asked him what role God played in
    the construction and regulation of the heavens. "Sire," Laplace
    replied, "I have no need of that hypothesis."

Additional matter, also by Tyson, from 
http://www.haydenplanetarium.org/tyson/read/2005/11/01/going-ballistic

	Modern analysis demonstrates that on timescales of hundreds of
	millions of years—periods much longer than the ones considered by
	Laplace—planetary orbits are chaotic. That leaves Mercury vulnerable
	to falling into the Sun, and Pluto vulnerable to getting flung out of
	the solar system altogether. Worse yet, the solar system might have
	been born with dozens of other planets, most of them now long lost to
	interstellar space. And it all started with Copernicus's simple
	circles. 

Does God obey Newton's laws?

God is still the author of the laws of nature, though even God is no longer
allowed to act in ways that "break" the laws.  Newton never accepted that the
laws are absolute in this way.  Though we can write eqns to descr these laws,
in what sense do such laws "exist" even before physical objects exist?  Or
what makes these laws applicable to all objects in space, without exception?

Newton's answer:  The laws exist in the mind of God even before creation. God
could compel planets to conform to such laws (or not, as God chose).  But if
God is removed, the laws of nature and the apparently necessary conformity of
physical objects to them becomes highly improbable and inexplicable. 30
[IDEA: Same problem remains with any theory - if X is the ultimate
explanation, we can always ask, "why X"? ]

Newton found it difficult to comprehend the force of gravity, though he had
virtually discovered it: That one body may act upon another at a distance
through a vacuum without the mediation of anything else ... is to me so great
an absurdity that I believe no man, who has in philosophical matters a
competent faculty for thinking, can ever fall into.
[Principia Mathematica tr Cohen / Whitman p. 943] 31

Newton wrote extensively on Hermetic philosophy and alchemy, and a long and
boring commentary on the prophecies in the Book of Daniel. 32
Westfall: Never at Rest: A biog of Isaac N 1980,
Mordechai Feingold: The Newtonian moment (beautifully produced
	  descripn of his cultural context).

Evolution and Religion

25 parameters such that values must fall within some range for life to
exist. [Hugh Ross, Creator and Cosmos, Navpress, 1993] p. 37

Biggest challenge from modern sci to religion is evolution.
But evoln can with equal plausibility be seen as a supremely elegant process
directed to goals of intrinsic value. 49

Evolutionary theory, with less sci evidence, existed well before Darwin -
e.g. his grandfather Erasmus Darwin, 1801: All nature exists in a state of
perpetual improvement ... the world may still be said to be in its infancy,
and continue to improve for ever and ever'.  [Zoonomia, Johnson, 1801, v.2,
p. 318) 50

Common belief in many traditional religions: Age of innocence, without
suffering or death - degraded into present corrupt state.  Evolutionary
theory reverses this judgment.  53
[Does it?  What is "suffering" - has it reduced?  Is the bacterium not a
"happier" organism? ]

Advances in morality in some societies : e.g. in attitudes to women, slaves,
and animals. 53
[Are these advances?]

Pensees and Pascal's wager

Pascal's Wager applies decision theory to the belief in God.  The
basic argument is that though the existence of God cannot be determined
through reason, a person should "wager" as though God exists, because
living thus, he has everything to gain, and should God not exist, he has
not much to lose.

Before Pascal's death at age 39, he was working on a text defending
Christian beliefs.  This was published later as Pensees (lit. "thoughts),
and the wager appears as Article 233 in Pensees.

Earlier, he laments man's uncertain position w.r.t. God:

	If I saw no signs of a divinity, I would fix myself in denial. If I
	saw everywhere the marks of a Creator, I would repose peacefully in
	faith. But seeing too much to deny Him, and too little to assure me, I
	am in a pitiful state, and I would wish a hundred times that if a God
	sustains nature it would reveal Him without ambiguity.[229]

then he measures the outcomes of believing in the two sides of this
uncertainty :

	Endeavour then to convince yourself, not by increase of proofs of God,
	but by the abatement of your passions. You would like to attain faith,
	and do not know the way; you would like to cure yourself of unbelief,
	and ask the remedy for it. Learn of those who have been bound like
	you, and who now stake all their possessions. These are people who
	know the way which you would follow, and who are cured of an ill of
	which you would be cured. Follow the way by which they began; by
	acting as if they believed, bless yourself with holy water, have
	Masses said, and so on; by a simple and natural process this will make
	you believe, and will dull you — will quiet your proudly critical
	intellect...

	Now, what harm will befall you in taking this side? You will be
	faithful, honest, humble, grateful, generous, a sincere friend,
	truthful. Certainly you will not have those poisonous pleasures, glory
	and luxury; but will you not have others? I will tell you that you
	will thereby gain in this life, and that, at each step you take on
	this road, you will see so great certainty of gain, so much
	nothingness in what you risk, that you will at last recognize that you
	have wagered for something certain and infinite, for which you have
	given nothing. [233]

Variations of this argument may be found in other religious philosophies,
such as Islam (al-Juwayni), and Hinduism (Vararuchi).

Blaise Pascal, _Pensees_, 1660, tr W. F. Trotter

Recent analysis of 3-body dynamics in the solar system

[Existence of poetentially collisional trajectories of Mercury, Mars and
Venus with the Earth;  Laskar and Gastineau, Nature, 817–819, 2009]

One of the interesting aspects of the solar system is that the orbits of
Mercury and Jupiter precess at the same rates - so their their apsidal lines
— the lines that connect the Sun to the point of closest approach of the
planetary orbit — are always in the same phase.  Based on extensive
simulations, Laskar and Gastineau have argued recently (fig above, 2009) that
this has a high probability of establishing a resonance which would pull the
eccentricity of Mercury’s orbit until it may cross that of Venus. Once orbit
crossing occurs, a variety of disastrous outcomes are possible...

So what would Pascal suggest we do?  Well, we have 5 billion years to think
about it.