Four ways

Following my review of the book Piranesi by Susanna Clarke, I wanted to say something about different ways of seeking knowledge. I see four fundamental options, which I list below, and illustrate graphically above (click to zoom).

P & P (agreement / synthesis)

I use the formula P & P to reflect the situation where different ways of thinking – such as Science, Art, and Religion – are all telling the same story, and therefore form part of a grand cultural synthesis. This was a characteristic of medieval thought in Europe, where Art frequently told religious stories, and Thomas Aquinas had integrated Religion with the best available Science of his day. Perhaps the pinnacle of the medieval approach is the poetry of Dante Alighieri (depicted above), where Religion and Science are combined together with poetic Art. But that was 700 years ago, of course.

P & Q (complementarity)

I use P & Q to reflect the situation where Science, Art, Religion, etc. are seen as complementary but incommensurable. They all produce their own kind of “truth” (P versus Q). I can study the stars, but independently of that, I can also see them as beautiful. For the case of Science and Religion, Stephen Jay Gould has called this approach non-overlapping magisteria.

The problem with this approach is a kind of fragmentation of life. Art is distinguished from Technology in ways that the ancient Greeks would have found bizarre. Increasingly, people seem to be fighting against this situation.

P > ~P (over-riding)

I use P > ~P to reflect the situation where Science, Art, Religion, etc. are seen as contradictory (P versus not P), but one source of “truth” is seen as superior to, and thus over-riding, the others. This includes the case of religious people who do not believe that observation of the universe can produce valid truth. It also includes scientism, or the belief that Science trumps everything else (a doomed approach, because the foundations of Science are themselves not scientific; they are philosophical and mathematical). I have illustrated this option with the depiction of Isaac Newton by William Blake. This was not intended to be a positive depiction; around about the same time Blake famously wrote “May God us keep / From Single Vision and Newton’s sleep.

The novel Piranesi touches on the problems of scientism: “It is a statue of a man kneeling on his plinth; a sword lies at his side, its blade broken in five pieces. Roundabout lie other broken pieces, the remains of a sphere. The man has used his sword to shatter the sphere because he wanted to understand it, but now he finds that he has destroyed both sphere and sword. This puzzles him, but at the same time part of him refuses to accept that the sphere is broken and worthless. He has picked up some of the fragments and stares at them intently in the hope that they will eventually bring him new knowledge.

P & ~P (contradiction / chaos)

Finally, I use P & ~P to reflect the situation where Science, Art, Religion, etc. are seen as contradictory (P versus not P) but the contradiction is embraced. Your “truth” may be completely contradictory to my “truth,” but that’s OK. The result of this is a kind of postmodernist chaos that seems to me fundamentally unstable. Indeed, former adherents of this approach seem now to be moving towards a new single dominant metanarrative.

So those are four ways of seeking knowledge. Can we indeed live with contradiction? Can the problems of complementarity be resolved? Or is it possible to construct some new synthesis of Science, Art, Religion, and other ways of seeking knowledge? The novel Piranesi raises some interesting questions, but gives no answers, of course.

Artwork from a Florentine artist, Ryan N. McFarlane/U.S. Navy, Auguste Rodin, William Blake, and Ivan Ayvazovsky.

Piranesi: a book review

Piranesi (2020) by Susanna Clarke

I have been reading a fabulous new book called Piranesi by Susanna Clarke, the author of Jonathan Strange & Mr Norrell. The title of her new novel is drawn from the Italian artist Giovanni Battista Piranesi, and it takes place within an enormous and magical flooded House that is reminiscent of some of Piranesi’s art. “The Beauty of the House is immeasurable; its Kindness infinite,” Susanna Clarke writes. Adding to the enjoyment of this wonderful novel has been a series of podcasts by Joy Marie Clarkson (starting here).

The Prisons – A Wide Hall with Lanterns by Giovanni Battista Piranesi (1745)

There are multiple references to the Narnia stories of C.S. Lewis. One example is the similarity of the Albatross scene to the one in The Voyage of the Dawn Treader. Another is the way that “Valentine Andrew Ketterley” of “an old Dorsetshire family” (Part 4) suggests Uncle Andrew Ketterley from The Magician’s Nephew: “The Ketterleys are, however, a very old family. An old Dorsetshire family ….”

Working through this novel, I’ve been repeatedly struck with a strange sense of déjà vu. Either Susanna Clarke and I read the same books, or she is revealing to me something that, in an inarticulate way, I already knew. Or possibly both. That said, some of the echoes I see to other books are, no doubt, coincidence.

Some fan art of mine, prompted by the novella Rain Through Her Fingers by Rabia Gale, which is set in a flooded city that Piranesi reminds me of

I am reviewing the novel here on ScientificGems because it has a lot to say about Science, Knowledge, and how to relate to the World: “I realised that the search for the Knowledge has encouraged us to think of the House as if it were a sort of riddle to be unravelled, a text to be interpreted, and that if ever we discover the Knowledge, then it will be as if the Value has been wrested from the House and all that remains will be mere scenery. The sight of the One-Hundred-and-Ninety-Second Western Hall in the Moonlight made me see how ridiculous that is. The House is valuable because it is the House. It is enough in and of Itself. It is not the means to an end.” (Part 2). This recalls something that C.S. Lewis wrote in The Abolition of Man: “For magic and applied science alike the problem is how to subdue reality to the wishes of men …” Indeed, Susanna Clarke makes us ask “is Science truly our friend?”

More specifically, Susanna Clarke argues against Reductionist views of the world, and the need to approach the objects of study with Love: “It is a statue of a man kneeling on his plinth; a sword lies at his side, its blade broken in five pieces. Roundabout lie other broken pieces, the remains of a sphere. The man has used his sword to shatter the sphere because he wanted to understand it, but now he finds that he has destroyed both sphere and sword. This puzzles him, but at the same time part of him refuses to accept that the sphere is broken and worthless. He has picked up some of the fragments and stares at them intently in the hope that they will eventually bring him new knowledge.” (Part 7)

One may count the petals of a violet, for example, and grind it up to extract the ionones and anthocyanins responsible for odour and colour. But something has been lost in so doing, and the resulting description does not exhaust everything that can be said about the flower. This problem is amplified for those who do not themselves experience the flower, but rely on descriptions by others.

The novel also references Plato and the importance of universals: “You make it sound as if the Statue was somehow inferior to the thing itself. I do not see that that is the case at all. I would argue that the Statue is superior to the thing itself, the Statue being perfect, eternal and not subject to decay.” (Part 6). As Lewis would say: “It’s all in Plato, all in Plato: bless me, what do they teach them at these schools!

Expanding on a statement by Tertullian (c. 160–225), Galileo famously said: “[Science] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.” (Galileo, Il Saggiatore, 1623, tr. Stillman Drake)

This is true, of course, but the House does not speak to us only in mathematical language.

Plato in the Musei Capitolini, Rome (photo: Marie-Lan Nguyen)

There is much more to be said about this wonderful novel. It concludes with a repetition of the words: “The Beauty of the House is immeasurable; its Kindness infinite.” There is a whole philosophy of Science there.

Goodreads rates the novel as 4.3 out of 5, and reviews of the novel are mostly glowing. The Guardian calls it an “elegant and singular novel” while the LA Review of Books says “a work of intellectual intensity.” It made the top ten fantasy novel list for the 2021 Locus Awards (although it did not win). I’m giving it four and a half stars. And let me say to my readers: “may your Paths be safe … your Floors unbroken and may the House fill your eyes with Beauty.

4.5 stars
Piranesi by Susanna Clarke: 4½ stars

What Mathematics is not

Just recently, I responded to a pair of viral videos by a 16-year-old TikTok user called Gracie Cunningham (her second video is here). Along with a lot of nasty abuse (Twitter is a cesspool), Gracie received many friendly, but in my view quite wrong, replies. So I thought I would say something about what mathematics is not.

1. Mathematics is not a language

Mathematics obviously includes a language, but mathematics is not just a language.

If you think about it, the “notation” section of mathematics textbook is kind of like a dictionary. But the bulk of a mathematics textbook makes (and proves) assertions. In this sense, a mathematics textbook is like a botany textbook or a physics textbook – it has content. It discusses mathematical objects, and makes statements about them.

2. Mathematics is not a cultural artefact that we invent

This should also be obvious. First, if mathematics was simply cultural, it would not be so enormously useful in science. Indeed, as Eugene Wigner famously pointed out, parts of mathematics are often useful in areas quite different from the area where they first arose. In particular, the number π = 3.14159… is useful all over the place.

Second, mathematicians are acutely aware that we can’t just “make things up.” In the words of Jacques Hadamard: “We speak of invention: it would be more correct to speak of discovery… Although the truth is not yet known to us, it pre-exists and inescapably imposes on us the path we must follow under penalty of going astray.”

Third, if mathematics was simply cultural, incompatible versions of mathematics would arise in different cultures, and this is not the case. For example, the picture below shows a sum in modern Western numerals, and the same sum in Devanagari numerals (from India), Chinese numerals, Mayan numerals (in base 20), and Babylonian numerals (in the base 60 that still survives in our hours, minutes, and seconds). The same truth (39 + 47 = 86) is expressed in all five systems, even though the notation for expressing that truth may differ.

3. Mathematics is not a set of empirical truths

This one is less obvious. Pure mathematicians tend to believe, with G. H. Hardy, “that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations.” Many physicists believe that mathematical truths are discovered from the physical universe, but pure mathematicians tend to believe that mathematical truths lie beyond the physical universe. As Saint Augustine put it, “The man who knows them [mathematical lines] does so without any cogitation of physical objects whatever, but intuits them within himself. I have perceived with all the senses of my body the numbers we use in counting; but the numbers by which we count are far different from these. They are not the images of these; they simply are. Let the man who does not see these things mock me for saying them; and I will pity him while he laughs at me.”

One reason why Hardy and Augustine have to be right is that we can imagine a different universe, with different physical laws. But no matter how different the universe, 39 + 47 = 86 would still be true. It is, somehow, true at a deeper level than the laws of physics.

Another reason is that the empiricist point of view isn’t true to the history of mathematics. Galileo used parabolas to describe the motion of falling objects, but the ancient Greeks had originally described parabolas in a quite different context, that of conic sections. Similarly, imaginary numbers were originally discussed without the slightest idea that centuries later they would become a fundamental part of quantum theory.

A third reason is that a great deal of mathematics has no connection to the physical universe at all. Mathematicians study the properties of numbers far larger than the number of particles in the universe, and the properties of algebraic structures with no (known) relationship to the physical universe. Usefulness of the mathematical truths they discover is the furthest thing from their minds. As Joel Spencer, put it, “Mathematics is there. It’s beautiful. It’s this jewel we uncover.”

Answering Gracie Cunningham

A 16-year-old TikTok user called Gracie Cunningham recently went viral with two short videos (second video here) asking questions about mathematics. Like a few other people, I thought that they were sufficiently interesting to answer.

1. How did people know what they were looking for when they started theorising about formulas? Because I wouldn’t know what to look for if I’m making up math.

Well, first, contrary to your comment “I don’t think math is real,” mathematics is indeed real. Even if the universe was completely different from the way it is, mathematics would still be true. Edward Everett, whose dedication speech at Gettysburg was so famously upstaged by Abraham Lincoln, put it like this: “In the pure mathematics we contemplate absolute truths, which existed in the Divine Mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven.” (OK, not everybody has this view of mathematics, which is called “Platonism,” but in my opinion, it’s the only view that explains why mathematics works).

Second, mathematics is discovered, not invented. The great mathematician G. H. Hardy pointed out “that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations.” When you embark on a journey of discovery, you don’t know where you’ll end up. That’s what makes it exciting. When the early Polynesians set off in canoes across the Pacific, thousands of years ago, they didn’t know that they would discover Hawaiʻi, Samoa, and New Zealand. They just headed off into the wild blue yonder because that was the kind of people they were.

Now the Babylonians and others developed mathematics primarily because it was useful – for astronomy (which you need to decide when to plant crops) and engineering and business. But the Greek started to do mathematics just for fun. They discovered mathematical truths not because they were useful, but simply because, as Joel Spencer, put it, “Mathematics is there. It’s beautiful. It’s this jewel we uncover” (quoted in The Man Who Loved Only Numbers, p 27).

It is also worth pointing out a subtle kind of prejudice (almost a kind of racism) that is widespread – many people think that the ancients were primitive. They weren’t. They had plumbing, and architecture, and astronomy. They even knew about zero. Some of them were very smart people. There were Babylonian versions of Albert Einstein, whose names are now long forgotten. There were many Greek versions of Albert Einstein (including Archimedes, among others). I kind of wish that schools would teach young people more about what the past was actually like. If people learn anything about the past at all, it’s usually from popular literature:

2. Once they did find these formulas, how did they know that they were right? Because, how?

Short answer: Euclid. Around about his time, the Greeks started to ask themselves exactly that question, and developed the concept of rigorous mathematical proof as an answer. The fact that typical mathematics classes don’t introduce simple proof is yet another indication of how badly broken modern education is. Even this simple visual proof (uploaded by William B. Faulk; click to view animation) gets the idea across:

3. Why is everyone being really mean to me on Twitter? Why are the only people who are disagreeing with me the ones who are dumb, and the physicists and mathematicians are agreeing with me?

Well, that’s also an interesting question. First, for reasons that I don’t fully understand, Twitter just makes people mean.

Second, as Dunning and Kruger famously pointed out, it is the people who know the least that are the most confident.

Third, the original video was in teen-girl English, with multiple uses of the word “like” (I have a sneaking suspicion that this was deliberate). Using teen-girl English for a “serious” subject like mathematics makes people’s heads explode (this will be useful to know when you have your first job interview).

But thank you, Gracie, for asking some really good questions.

Some follow-up remarks on what mathematics is not are here.

Seven varieties of metaphysics

I was having a discussion with someone recently on metaphysics, so I thought I would blog about it. Here are seven varieties of metaphysics, describing three “layers” of reality (and yes, I am oversimplifying for brevity).

The first is Platonism. Plato believed that there was a hierarchy of Forms (Ideals), of which the highest was The One (Plato’s version of God). These Forms or Ideals were the true reality, and the physical objects we touched, saw, and tasted were only shadows of that true reality (that is the point of the allegory of the cave). The physical orange which we see and eat reflects Ideals such as “Fruit,” “Sphere,” and “Orange.” Neoplatonism continues and extends this point of view.

Saint Augustine and many later Christians held to a Christianised Platonism, in which the Ideals were thoughts in the mind of God (the Christian God, naturally). The physical objects we touched, saw, and tasted had a greater importance in Christian Platonism than they did for Plato – after all, when God created those objects, “God saw that it was good.” Much as with Platonism, the regularities that people see in the physical universe are explained by the fact that God created the universe in accordance with regularities in the Divine thoughts. However, Christian Platonism does not have the metaphysical hierarchy that Platonism or Neoplatonism have – in Christian Platonism, God makes direct contact with the physical universe.

Aristotle also reacted to Plato by increasing the importance of the bottom layer, and Aristotle’s thought was Christianised by Thomas Aquinas as Thomism. However, in Thomism the all-important bottom layer does very little except to exist, to have identity, and to have properties assigned to it. It is also not observable in any way. This can be seen in the Catholic doctrine of transubstantiation. According to the Tridentine Catechism of 1566, the bread and the wine of the Eucharist lose their bottom (“substance”) layer (“All the accidents of bread and wine we can see, but they inhere in no substance, and exist independently of any; for the substance of the bread and wine is so changed into the body and blood of our Lord that they altogether cease to be the substance of bread and wine”), while the bottom (“substance”) layer of the body and blood of Christ becomes metaphysically present instead.

Idealism denies that the physical universe exists at all. The followers of Mary Baker Eddy take this view, for example, as did George Berkeley. Only thought exists. To quote a famous movie line, “there is no spoon.” These thoughts may be independent of whatever God people believe in or, as in monistic Hinduism, they may be actually be the thoughts of God (in which case, only God exists).

The last three kinds of metaphysics deny the existence of any kind of God. In Platonist Materialism, this denial is combined with a Platonist approach to mathematics, about which I have written before. Mathematics exists independently of the physical universe, and controls the physical universe, in the sense that the physical universe follows mathematical laws. Roger Penrose is one of many scientists holding this view.

In what I am calling Extreme Materialism, the existence of an independent mathematical world is also denied, i.e. there is an empiricist approach to mathematics (mathematics simply describes observed regularities in nature). This view seems to be increasing in popularity among non-religious people, although it causes philosophical problems for mathematics.

Finally, the concept of the Mathematical Universe holds that the so-called “physical universe” is itself composed only of mathematical objects – only mathematics exists (which makes this, in fact, a kind of Idealism).

On fairy tales

“About once every hundred years some wiseacre gets up and tries to banish the fairy tale,” C.S. Lewis wrote in 1952. The wiseacre of our time seems to be Richard Dawkins who, two years ago, told the world that fairy tales could be harmful because they “inculcate a view of the world which includes supernaturalism” (he had said similar things in 2008). In a later clarification, he added that fairy tales could “be wonderful” and that they “are part of childhood, they are stretching the imagination of children” – provided some helpful adult emphasises that “Do frogs turn into princes? No they don’t.”

But many scientists grew up with, and were inspired by, fantasy literature. For example, Jane Goodall tells of growing up with the novel The Story of Doctor Dolittle (as I did!). In fact, many science students and professional scientists avidly read fantasy literature even as adults (as they should). The booksthatmakeyoudumb website lists, among the top 10 novels read at CalTech and MIT, Harry Potter, Dune, and The Lord of the Rings. And Alice in Wonderland was written by a mathematician.

This is a science blog, so I have a strong emphasis on scientific truth, which tells us many important ecological and physiological facts about, for example, frogs. Without science, we’d all still be struggling subsistence farmers. But there is actually more than scientific truth out there.

There is also mathematical truth. Are the links in this frog network all equivalent? Yes, they are – but that is decided by mathematical proof, not by scientific experiment. It is in fact a purely abstract mathematical question – the background picture of the frog is actually irrelevant.

And there is ethical truth. Is it OK to eat frog’s legs? Science does not give us the answer to this (although logic can help us decide if our answer is consistent with our other beliefs), but fantasy literature often helps us to explore such ethical questions. Tolkien’s The Lord of the Rings is one superb example. Would you “snare an orc with a falsehood”? Would you attempt to take the One Ring and “go forth to victory”?

There is metaphorical truth. A frog may, in spite of what Dawkins says, be a handsome prince – there’s more to the universe than can be seen at first glance. Or, as Antoine de Saint-Exupéry put it, “What is essential is invisible to the eye.” Children often learn this important fact from fairy tales.

And there is even religious and philosophical truth. Does the frog-goddess Heqet exist, for example? Does the universe exist? Is there a spoon? The methods of philosophy are different from the methods of science, and some amateur philosophers simply state their beliefs without actually justifying them, but philosophy is actually very important. Science itself is based on certain philosophical beliefs about reality.

God’s Philosophers: a book review

God’s Philosophers by James Hannam (2009)

I recently read James Hannam’s God’s Philosophers, which is the story of the Medieval ideas that led up to modern science, told largely through short biographies of major and minor figures (this relates to my previous two posts about when and why science began, as well as to my three posts about science and Dante).

Farming in the 15th Century

The early Middle Ages was, to a large extent, a struggle to build a more productive agricultural system (since Europe had lost access to the rich grain-fields of North Africa that had fed the Roman Empire). The later Middle Ages, however, saw an explosion of new ideas. Some of these ideas came from the Muslim world, but many were entirely original.

The Age of Cathedrals: Bourges (begun c. 1195, finished c. 1230)

Hannam briefly surveys Medieval mathematics, logic, medicine, astronomy, astrology, alchemy, and engineering. Roger Bacon (1214–1292) and Richard of Wallingford (1292–1336) are discussed in some detail. The former wrote on optics and the theory of science, while the latter did work in trigonometry and designed an elaborate astronomical clock. Clocks were to replace living things as metaphors for the operation of the Universe.

Richard of Wallingford using a pair of compasses

Hannam also has a chapter on the Merton CalculatorsThomas Bradwardine (c. 1290–1349), Richard Swineshead (fl. 1340–1355), and William Heytesbury (c. 1313–1373). As well as contributing to logic, these scholars anticipated Galileo’s application of mathematics to physics, proving the mean speed theorem. In France, Nicole Oresme (c. 1325–1382) developed an elegant graphical proof of this theorem, as well as doing work in astronomy and introducing the bar graph. Ironically, it was the later Humanists who, inspired by the glories of ancient Greece and Rome, discarded some of these advances (the same source of inspiration also led to a decline in women’s rights, as Régine Pernoud has pointed out).

Merton College, Oxford (Michael Angelo Rooker, 1771)

Hannam finishes his book with the stories of Kepler and Galileo. These are better known than those of the Medievals, but the myths surrounding Galileo seem to be as persistent as those about the so-called “Dark Ages.” Hannam’s treatment is necessarily simplistic and brief, but he does point out Galileo’s debt to Oresme and the Merton Calculators. For readers specifically interested in Galileo, the best introductory book is probably Galileo’s Daughter by Dava Sobel, with Finocchiaro for follow-up.

Although Galileo pitted the modern Copernicus against the ancient Ptolemy, Tycho Brahe had already suggested a hybrid system, which was only later proved wrong

Hannam concludes “It would be wrong to romanticise the period and we should be very grateful that we do not have to live in it. But the hard life that people had to bear only makes their progress in science and many other fields all the more impressive. We should not write them off as superstitious primitives. They deserve our gratitude.

See also this review in Nature of Hannam’s book (“God’s Philosophers condenses six hundred years of history and brings to life the key players who pushed forward philosophy and reason”), this review by a Christian blogger (“In God’s Philosophers James Hannam traces medieval natural philosophy—and some of the other disciplines we’ve come to think of as scientific, such as medicine—through the reign of Plato and Aristotle to the discoveries of Kepler and Galileo”), and this excellent review by an atheist historian (“… the myth that the Catholic Church caused the Dark Ages and the Medieval Period was a scientific wasteland is regularly wheeled, creaking, into the sunlight for another trundle around the arena. … Hannam sketches how polemicists like Thomas Huxley, John William Draper, and Andrew Dickson White, all with their own anti-Christian axes to grind, managed to shape the still current idea that the Middle Ages was devoid of science and reason.”). Hannam has also responded comprehensively to this negative review by Charles Freeman. I disagree with Freeman, and am giving Hannam’s well-researched and readable book four stars. My only real quibble is Hannam’s somewhat biased view of the Protestant Reformation.

* * * *
God’s Philosophers by James Hannam: 4 stars

The Universe: four philosophical views

View 1. The Universe does not exist

This first philosophical view is familiar through the slogan “there is no spoon.” The only true reality, it says, is spiritual. Nothing physical actually exists. This view has been taught by some (though not all) schools of Hinduism. In Europe, it is associated with George Berkeley. The difficulty with this perspective is that the laws of science must, in some sense, be emergent from the spiritual reality. But how?

View 2a. The Universe exists, but has not always existed

This view implies a time t0 at which the Universe “began” – in the sense that nothing (not even time) existed before then. The immediate response is: why? Some kind of explanation for the existence of the Universe seems necessary (although Stephen Hawking argues not). Given that there could be no event before t0, a purely scientific explanation seems impossible, leaving religion or philosophy to supply one. The traditional explanation – from Plato, Christianity, and other religions – is some form of divine creation. Such an explanation is not everybody’s cup of tea, of course.

View 2b(i). The Universe has always existed, with a finite number of states

Alternatively, the Universe has always existed. If the number of possible states in the Universe is finite, this means that the present state of the Universe must have occurred infinitely often in the past (down to the position of every atom), and must occur infinitely often in the future. Previous analogues of me have blogged this comment infinitely often in the past, and infinitely many future analogues will do so again. This is true whether the Universe is deterministic or random. The Stoics were one group who believed in such a (rather depressing) cyclic Universe, but it seems difficult to swallow.

View 2b(ii). The Universe has always existed, with an infinite number of states

The prospect of “eternal recurrence” can be eliminated if the Universe has an infinite number of states, but this seems to require some kind of eternal expansion. The Steady State model was once proposed as a way of achieving this. A modern alternate suggestion is that new sub-Universes are constantly “popping into existence” as a result of quantum fluctuations in older sub-Universes, thus forming an infinite branching tree.

It is not quite clear how this branching would work, however, and Paul Davies points out that there are philosophical problems too: “For a start, how is the existence of the other universes to be tested? To be sure, all cosmologists accept that there are some regions of the universe that lie beyond the reach of our telescopes, but somewhere on the slippery slope between that and the idea that there are an infinite number of universes, credibility reaches a limit. As one slips down that slope, more and more must be accepted on faith, and less and less is open to scientific verification. Extreme multiverse explanations are therefore reminiscent of theological discussions. Indeed, invoking an infinity of unseen universes to explain the unusual features of the one we do see is just as ad hoc as invoking an unseen Creator. The multiverse theory may be dressed up in scientific language, but in essence it requires the same leap of faith.

So there you have it. Four views, some of which have been around for millennia, and all of which have adherents and opponents. View 2a is the most commonly accepted. Which one do you think is correct?

Evolution as a Religion: a book review

Evolution as a Religion: Strange Hopes and Stranger Fears by Mary Midgley (1985, revised edition 2002)

I recently read the classic Evolution as a Religion: Strange Hopes and Stranger Fears by English philosopher Mary Midgley. In the introduction to the revised (2002) edition, Midgley explains the motivation for the book as follows: “I had been struck for some time by certain remarkable prophetic and metaphysical passages that appeared suddenly in scientific books about evolution, often in their last chapters. Though these passages were detached from the official reasoning of the books, they seemed still to be presented as science. But they made startling suggestions about vast themes such as immortality, human destiny and the meaning of life.” (p. viii). As an example, she quotes the molecular biologist William Day: “He [man] will splinter into types of humans with differing mental faculties that will lead to diversification and separate species. From among these types, a new species, Omega man, will emerge … as much beyond our imagination as our world was to the emerging eucaryotes.” (p. 36).

Mary Midgley

Such “prophetic and metaphysical passages” are also familiar from the fictional works of Olaf Stapledon and H. G. Wells. Midgley argues that they represent bad science, twisted to have characteristics of a religion, such as assigning meaning to life (pp. 15, 71). The myth of the “Evolutionary Escalator,” extrapolated to some glorious imaginary future, is one example. Nothing in evolutionary science justifies this view, comforting though it may seem (p. 38). Furthermore, past attempts to accelerate the process by breeding an “Übermensch” have not ended at all well (p. 9), and more recent proposals are also disturbing (pp. 48–49).

The “Evolutionary Escalator” or “March of Progress”

Midgley claims that prophecies based on the “Evolutionary Escalator” myth “are quite simply exaltations of particular ideals within human life at their own epoch, projected on to the screen of a vague and vast ‘future’ – a term which, since Nietzsche and Wells, is not a name for what is particularly likely to happen, but for a fantasy realm devoted to the staging of visionary dramas. In their content, these dramas plainly depend on the moral convictions of their author and of his age, not on scientific theories of any kind.” (pp. 81–82).

In contrast, Midgley quotes a more pessimistic perspective from the physicist Steven Weinberg: “The more the universe seems comprehensible, the more it also seems pointless. But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desk for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.” (pp. 86–87). This perspective is very different from that of the evolutionary optimists, but it does share a certain scientist-centric bias.

Tho’ Nature, red in tooth and claw
With ravin, shriek’d against his creed, –

Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life;

‘So careful of the type?’ but no.
From scarped cliff and quarried stone
She cries, ‘A thousand types are gone:
I care for nothing, all shall go.’

(from Alfred, Lord Tennyson, In Memoriam A.H.H., LIV and LV)

Midgley is particularly negative about the “red in tooth and claw” view of evolution, which emphasises competition as against cooperation. She sees the “selfish gene” concept popularised by Richard Dawkins as an example of this. In a 2007 interview with The Independent, she claimed “The ideology Dawkins is selling is the worship of competition. It is projecting a Thatcherite take on economics on to evolution. It’s not an impartial scientific view; it’s a political drama.

Honeybees are great cooperators (photo: Todd Huffman), and symbiosis is common in nature

Indeed, when an organism succeeds by occupying a new ecological niche (as, for example, urban coyotes do), there need not be any competition at all (at least, not initially).

A coyote in an urban niche (photo: Dru Bloomfield)

Extreme forms of sociobiology comes in for particular criticism from Midgley. They produce, she claims, bad science: “Environmental causes are neglected without any justification being given, and so are causes which flow from an individual itself during its lifetime … In human affairs, both these areas are of course of the first importance, since they cover the whole range of culture and individual action.” (p. 151). She is far from being the only scholar to make such criticisms.

Less common is the way in which she blames the growth of creationism on the rhetoric of sociobiologists themselves: “The project of treating the time scale of the Genesis story literally, as a piece of history, is an amazing one, which serious biblical scholars at least as far back as Origen (AD 200) have seen to be unworkable and unnecessary. The reason why people turn to it now seems to be that the only obvious alternative story – evolution – has become linked with a view of human psychology which they rightly think both false and immoral.” (p. 172).

See also this talk by Midgley, related to a more recent book on a similar topic:

In essence, Mary Midgley strongly supports scientists when they do science, but does not always accept the results of scientists doing philosophy (and especially moral philosophy). This little book sounds a helpful note of caution for those scientists who have become interested in philosophical speculation.

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Evolution as a Religion, by Mary Midgley: 4 stars