A Speaker for Stephen Hawking (1942-2018)

De mortuis nil nisi bonum dicendum est
(Say nothing about the dead unless good)


I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.
–Stephen Hawking, The Nature of Space and Time (1994)

Praise for a First-Rate Scientist, a Fighter against a Crippling Handicap

I learned about Stephen Hawking’s death Tuesday, 14th March, reading my favorite news digest, “The Drudge Report”, which cited this Daily Mail article. The comments after the article were uniformly laudatory, endowing him with the status of  “the Einstein of our generation,” a great philosopher, a fighter against a crippling handicap, a man of humor and kindness.  The first and second of those appraisals I regard as excessive, the third I agree with, and the fourth–I don’t know.

What I will attempt in this post is to be a “Speaker for the Dead”, emulating Ender Wiggins, the hero of Orson Scott Card’s Ender’s Game Quintet.  Wiggins travelled the galaxy giving not eulogies, but honest appraisals of people who had died, appraisals that both honored the dead more than a conventional eulogy and ultimately were more comforting to those who grieved for the departed.

I’ll discuss Hawking’s popular works on science, his principal scientific works (and how his viewpoint seems to have changed in his later years), and his views on religion (which also seem to have changed in his later years).  I won’t discuss his private life, other than to say that if you read the Daily Mail article carefully, you might have a plot for a good TV show–oh wait, that has been made–see, “The Theory of Everything.

Writing something that might be regarded as even mildly critical of Hawking (particularly of his scientific work) puts me im the position of a Lilliputian shooting arrows at Gulliver.   Nevertheless, even though some of the math in Hawking’s work is above my pay-grade, I’m familiar enough with most of the math and with the subject  to evaluate (I’ve read related works by Penrose and Ellis); moreover, I have a background as a physicist (non-theoretical) and from readings in the philosophy of  science sufficient to apply the comment Hawking gave in the opening quote.

“A Short History of Time” and Other Popular Works

Let’s turn to Hawking’s  popular works on science, written for the non-scientist.   The most famous of these is “A Short History of Time,” a best seller (over 10 million purchased).   Some wag (whose name I don’t recall) said about this book “that next to the Bible, it’s been purchased by more people who’ve never finished reading it than any other.”   I did finish reading it (“A Short History of Time,” as well as the Bible);  it’s a fine book; Hawking does  a great job  explaining the science basic to cosmology.   I particularly like a quote at the end of the book on why the Universe exists:

“If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God”\
–Stephen Hawking, “A Short History  of Time”

I’ll comment on this quote below, in the discussion of Hawking’s religious and political views.

Other popular works by Hawking have sold well, although not as well as “A Short History of Time:”

“The Universe in a Nutshell,” a sequel to “A Short History…,” which discussed new developments in theoretical physics occurring after the publication of that work;

“On the Shoulders of Giants,” a collection of original papers and essays on ground-breaking scientists: Copernicus, Galileo, Newton and Einstein;

“God Created the Integers,” a collection of original works by famous mathematicians: Euclid, Archimedes, Diophantus, Descartes, Newton, Euler, Laplace, Fourier, Gauss, Cauchy, Lobachevsky, Bolyai, Galois, Boole, Riemann, Wierstrass, Dedekind, Cantor, Lebesgue, Gödel, and Turing, and commentary;

“The Grand Design,” co-authored with Leonard Mlodinow, a work of evangelical atheism that proposed gravity as the creator of the universe (I’ll comment more about this book below),

If you read negative reviews on Amazon.com of the second and third of those listed, you’ll find criticisms not of what Hawking wrote, but of typographical errors in the selected papers.  I should note that he also wrote an autobiography and several science-fiction books for children, coauthored with his daughter, Lucy Hawking.

Stephen Hawking’s Science: 1) Singularities and Black Holes

The featured image is an artist’s depiction of a black hole, with gravitational lensing rings surrounding it.   This phenomenon is what the public associates with Hawking, although the term “black hole” was in fact coined by the American theoretical physicist, John Wheeler.  Black Holes are thought to represent “singularities” in space-time, caused by collapse of giant stars.   Such singularities are found in solutions of Einstein’s field equations (partial differential equations) for general relativity.   In a naive and simple way, one can think of a singularity as a region where a solution blows up to infinity: for example, if in a solution, 1/r, r  were equal to zero and 1/r would be infinite.

Hawking’s publication list shows that his research, from the time he received his Ph.D from Cambridge University until his later years, focused on cosmological singularities, black holes and the formation of the universe.  The major opus resulting from this research was the Hawking-Penrose Singularity Theorem, published in 1970.   This followed the first general treatment of singularities from a topological approach, given by Roger Penrose in 1965.

Why are singularities more than just a mathematical curiosity?   They show how (in the framework of general relativity) gravitation produces singularities.   And these singularities are the wrinkles in space-time that give rise to black holes, and again, in the framework of general relativity, the creation of the universe, “The Big Bang.”    The black hole singularity comes about when gravity is so strong that matter is compressed to a single point;  the hole is black because the speed of light is slowed down by gravity so much that it cannot escape the boundaries of the black hole (“the event horizon”).

Stephen Hawking’s Science: 2) The Entropy of Black Holes

Anything with mass (say the space ship Enterprise) has entropy.   If the Enterprise were to fall into a black hole, its entropy would disappear and  the entropy of the universe would decrease, thereby violating the Second Law of Thermodynamics, unless….the entropy of the black hole were to increase by an amount equal to or greater than that of the spaceship’s entropy.   Thus, that most rock solid of all scientific laws, the Second Law of Thermodynamics, requires that black holes have entropy.

In 1973 the Israeli-American physicist Bekenstein gave a formula for this entropy in terms of fundamental constants and A, the area encompassing the event horizon of the black hole.


where S is the entropy of the black hole, A the area bounded by the event horizon, c the speed of light, h Planck’s constant and G, the gravitational constant.

In 1974 and 1975 Hawking published work in which he combined quantum mechanics and general relativity to show that black holes could radiate energy like a black body, and that they did indeed, as Bekenstein had argued, have an entropy proportional to the area covered by the event horizon.   This prediction of “Hawking radiation” from black holes is regarded as possibly Hawking’s greatest work.  The equation above, in different forms, has become known as the BHE equation for entropy, where BHE may be taken to stand Bekenstein-Hawking Entropy or Black Hole Entropy.   I’ve read (can’t recall the reference) that Hawking wanted that formula on his tombstone, possibly emulating Stefan Boltzman who had his formula for entropy, S=klnW, relating the molecular and macrosopic world, engraved on his tombstone.

There have been controversies and seeming paradoxes about information as it’s related to black hole entropy.  However, perhaps the most interesting point is that there has never been an experimental confirmation of theoretical thermodynamics of black holes:

“The robustness of these thermodynamic properties of black holes under various theoretical considerations thus inspires a great deal of confidence in them. Yet none of these properties has ever been empirically confirmed. So given this lack of direct observations of Hawking radiation or of any other empirical signatures of the thermodynamics of black holes…”
–Christian Wuthrich, “Are Black Holes about Information”

Hawking’s Science: 3) A Universe with No Big Bang

Theoretical physicists who don’t believe in God don’t dislike singularities in general (witness the interest in black holes), but they do dislike the singularity at the beginning, “The Big Bang”, because it is consistent with belief in a Creator (uppercase C).   Accordingly, these atheists propose all sorts of unverifiable schemes–“baby universes,” eternal inflation, a multiuniverse, etc…–that do away with The Big Bang as a creation event.

Another way to dispense with the Big Bang was put forth by Hartle and Hawking in their no boundaries universe paper.  Hawkings had argued that general relativity could not be applied to a hypothetical t=0 (or near then) state of the universe because distances were so small that quantum mechanics had to be used–macroscopic dynamics, General Relativity, would not apply at distances corresponding to the size of particles and subatomic particles.  Accordingly, Hartle and Hawkings applied the DeWitt-Wheeler formulation for the wave-function of the universe with a very important change:  the time variable was changed from a real variable (real in the mathematical sense) to an imaginary variable–“new” time t = i x”old” time t;  here “i” = √-1.   The consequence of this change of time variable is that an initial condition, t=0, is no longer required for a solution to the Schrodinger equation from which the universe wave-function is to be derived;  hence, the “no boundary” universe (no time boundary); time becomes a space-like variable.

I have two criticisms to make of this proposal: first, it is not science, it is what I would term “mathematical metaphysics.”   There is no way to verify it (or falsify it) empirically; second, at some point the imaginary variable,  “t√-1,” has to change to a real variable t;  when, how and why would this occur?

Hawking Becomes an Evangelical Atheist

Hawking’s quote about “knowing the mind of God” was cited above, as was the title of his book about the history of mathematics, “God Made the Integers.”   Also reported (sorry, I can’t locate the source) was his attendance at a  Pasadena Episcopal Church during his stay at Caltech in the 1970’s.  At any rate, Hawking later said that his quote from “A Short History of Time” was only a figure of speech and made his position as an atheist quite clear:

“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.

In his book “The Grand Design,” co-authored with Leonard Mlodinow,  Hawkings argued that God was not necessary as an agent to create the universe out of nothing;  rather gravity did that.  He also proposed that M-theory (another form of string theory) explained the workings of the universe, that it was “The Theory of Everything.”   I won’t here try to refute these propositions;  criticisms by famous scientists are given in the linked article; for an exhausting critique of the philosophical and theological fallacies of the work, see these videos by Fr. Robert Spitzer, S.J. and Bishop Robert Barron.

The advocacy of string theory and the doing away with General Relativity at t=0, marks a decided change from Hawking’s position expressed in 1994:

“It [General Relativity] may require modifications on the Planck scale but I don’t think that will affect many of the predictions that can be obtained from it. It may be only a low energy approximation to some more fundemental theory, like string theory, but I think string theory has been over sold…My second reason for not discussing string theory is that it has not made any testable predictions. [emphasis added] By contrast, the straight forward application of quantum theory to general relativity, which I will be talking about, has already made two testable predictions. …Neither of these predictions will be changed even if string theory is the ultimate theory of nature. But string theory, at least at its current state of development, is quite incapable of making these predictions except by appealing to general relativity as the low energy effective theory. I suspect this may always be the case and that there may not be any observable predictions of string theory that can not also be predicted from general relativity or supergravity. If this is true it raises the question of whether string theory is a genuine scientific theory. Is mathematical beauty and completeness enough in the absence of distinctive observationally tested predictions. Not that string theory in its present form is either beautiful or complete. [emphasis added]
Stephen Hawking, “The Nature of Space and Time”

And please look again at the opening quote from this work by Hawking, in which he states the need for empirical confirmation of a scientific theory.

Final Remarks

This review of Hawking’s work (not his life) is perhaps biased by my opposition to his later position as an evangelical atheist.  It is also biased by my opposition to his political stance as an advocate of left-wing causes:  as a post from Washington Free Beacon, would have it

“But no amount of scientific greatness can excuse his political crusading—far left, viciously anti-Israel, and contemptuous of the culture and values that sustain western societies.” 
Noah Pollak, “Stephen Hawking wrote a popular book about physics and spent the rest of his life crusading for awful causes” The Washington Free Beacon,  March 15, 2018.

I believe the title of that article is extreme; Hawking did much fine work after the publication of “A Short History…”

I’m not going to comment on the disease, ALS, that severely limited Hawking’s mobility and speech. A good analysis is given by Dr. Leo McCluskey, University of Pennsylvania Medical School of how it might be that Hawking escaped the usual fate of those suffering  from ALS, an early death. One might wonder (and I don’t know the answer) whether ALS hindered or in fact enhanced Hawking’s career and reputation.

I will say finally that he was a brilliant, imaginative physicist.  Unfortunately most of the work he did and the theories he proposed, even the most famous–Hawking radiation–have not been, and perhaps never will be, subject to empirical verification or falsification.  He ranks in the forefront of contemporary theoretical physicists, but he was not of the stature of Einstein or those brilliant minds that  founded quantum theory.   As the Wikipedia article on “The Grand Design” suggests, his stature among the lay public is perhaps higher than that among the cohort of theoretical physicists, even though–as the comments after his death show–he was personally and professionally esteemed.



Once Again, Real Life Imitates South Park

Some of you no doubt find South Park to be a bit crude and maybe even offensive.  But I am constantly amazed at how often their satires run so true to real life.  Case in point: Stephen Hawking.  In a recent interview with the Guardian Stephen Hawking had this to say:

The universe is governed by science. But science tells us that we can’t solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value.

This caused Carl Olson to quip that Hawking “does, in fact, believe in and worship a god—the name of which is ‘Science'”.

That brought to mind the twopart episode from season ten where Cartman travels into the future and discovers an Earth where everyone is now an atheist (content warning).  Exclamations of “Science help us!” escape from everyone’s lips in times of trouble.

I’m not going to read too much into the South Park episodes, but they hint at a larger truth.  Even atheists cannot escape religion.  Near our house is something called the Washington Ethical Society.  We used to drive by this place when we went to Mass in the city, and they hold weekly meetings every Sunday.   Yes, it is essentially a Church for atheists.  Frankly, one would think that one of the “benefits” of being an atheist is not having to go to Church on Sunday, but for these atheists they can’t escape the Sunday obligation.  I don’t know if they sing hymns to science but I’m sure their gatherings are something to behold.

At any rate, there’s more from Olson as well as Msgr. Charles Pope on Hawking’s philosophy.  Msgr. Pope is troubled by where Hawking’s philosophy trends (the part in bold is from the article, the rest is Msgr. Pope):

When asked what is the value of knowing why are we here, Hawking replied, “The universe is governed by science. But science tells us that we can’t solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value.” This is so limiting. It is also philosophy, not science to say this. Mr Hawking is entitled to have a philosophy, but when he says the world is “governed by science” and then goes on to philosophize, that looks pretty silly and contradictory. Further, Mr. Hawking, if you ask me, is edging dangerously close to eugenics in what he says here. What exactly assigning a “higher value” to certain societies looks like as a practical matter is uncertain in what he says, but I sense a growing darkness here, not light. Margaret Sanger and Adolph Hitler may well be smiling as he says this. BEWARE!

The first commenter objected to Msgr. Pope’s anaology*, but it happens to be spot on.  Readings Hawking it is tough not to draw another cultural analogy, this time to C.S. Lewis’s That Hideous Strength.  That novel is the third part of Lewis’s space trilogy, and the plot revolves around the British Government’s new scientific institute, the National Institute for Coordinated Experiments (NICE).  The institute does some awful stuff in the name of science and progress, and the novel itself serves as a warning against the utopian promises of over-eager rationalists.

Hawking might be a brilliant physicist, but he should leave theology to the grownups.

* On a tangential note, I find myself getting more agitated by a trend in comments sections.  Why do people feel that they can completely discard the rules of grammar, capitalization and punctuation when they write comments on blogs?  The commenter on Msgr. Pope’s blog – the inaptly named Sophia – decided to take the opportunity to insinuate that atheists were smarter than religious people, all the while failing to capitalize a single word in her screed.  Why should I take anyone seriously when they can’t even obey the simple rules of the English language?  No, we’re not writing dissertations here, but if you can’t even be bothered to hit the shift key before typing the first letter of the first word of your sentences, then I will automatically discount anything you have to say.  I can understand typos as I’m sure there might be one or two above, and I’m not a perfect grammar student.  But can you at least make an effort to write properly on a discussion forum?

/End rant.