Dante’s Heaven

In previous posts (Inferno, Purgatorio, Paradiso), I have mentioned the scientific content of Dante’s incredible theological poem, the Divine Comedy. Above, just for fun, is a chart of Heaven (the Solar System) in his Paradiso. Notice the sphere of fire which was believed to surround the Earth.


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.


Out of the Silent Planet: a book review

Since Mars is on my mind right now…


Out of the Silent Planet (1938) by C. S. Lewis (1996 cover by Kinuko Craft)

C. S. Lewis is famous for the Narnia novels, but more than a decade before they were written, he published Out of the Silent Planet. Lewis was to write two sequels (I have blogged about the last volume, That Hideous Strength). However, Out of the Silent Planet is essentially science fiction, while the sequels are better described as fantasy.

Considered as a work of science fiction, Out of the Silent Planet was a pioneering novel. It followed (and was influenced by) novels by H. G. Wells, David Lindsay, and Olaf Stapledon, but preceded the work of Brian Aldiss, Arthur C. Clarke, and other British science fiction authors of the “Golden Age.” Lewis’s novel was one of the first to sound a cautious note about human colonisation of other planets. In his 1958 essay “Religion and Rocketry,” Lewis describes the rather sad results that human colonisation could have: “We know what our race does to strangers. Man destroys or enslaves every species he can. Civilized man murders, enslaves, cheats, and corrupts savage man. Even inanimate nature he turns into dust bowls and slag-heaps. There are individuals who don’t. But they are not the sort who are likely to be our pioneers in space.

Lewis’s word hnau (sentient being) was borrowed by James Blish in his alien-contact novel A Case of Conscience. In Out of the Silent Planet, Lewis brings colonisation to a halt after three deaths; Ursula K. Le Guin’s novel The Word for World Is Forest is one of many where exploitative colonisation runs its course. Several ideas in the 2009 film Avatar can be traced back to classic novels that were, in turn, ultimately inspired by Lewis.

In Out of the Silent Planet, Lewis introduces not one, but four, sentient species living in harmony with each other: the hrossa (farmers and poets), the séroni (scientists and philosophers), the pfifltriggi (artists, miners, and engineers), and the eldila (angels, essentially).

The scientist Weston actually recommends exterminating the inhabitants of the planet to make room for humans, claiming “Your tribal life with its stone-age weapons and beehive huts, its primitive coracles and elementary social structure, has nothing to compare with our civilization – with our science, medicine and law, our armies, our architecture, our commerce, and our transport system which is rapidly annihilating space and time. Our right to supersede you is the right of the higher over the lower. Life … is greater than any system of morality; her claims are absolute. It is not by tribal taboos and copy-book maxims that she has pursued her relentless march from the amœba to man and from man to civilization.” (this was an idea seriously suggested in the 1920s and 1930s, but one which was perhaps seen for what it was after World War II). The businessman Dick Devine simply wants to exploit the inhabitants for profit. Only the hero, Elwin Ransom, is interested in them for who they are.


Lewis wrote Out of the Silent Planet while a Fellow at Magdalen College, Oxford.

The science in Out of the Silent Planet is surprisingly good, considering that Lewis’s area of expertise was English literature. No doubt Lewis ran his ideas past the scientists at Magdalen College. There are some clangers in Lewis’s discussion of gravity onboard the spacecraft, and he no doubt knew that the theory of Martian canals was obsolete (although Robert A. Heinlein and Ray Bradbury were still using the idea of canals in the 1940s and 1950s). Lewis does an excellent job of explaining the impact of low gravity on Martian life, of pointing out that space is not “dark and cold,” and of describing the need for oxygen on the Martian surface.

He learned from the sorn that he was right in thinking they were near the limits of the breathable. Already on the mountain fringe that borders the harandra and walls the handramit, or in the narrow depression along which their road led them, the air is of Himalayan rarity, ill breathing for a hross, and a few hundred feet higher, on the harandra proper, the true surface of the planet, it admits no life.

Bringing in a specialist linguist (Elwin Ransom) to decipher the Martian language is a neat trick (and one repeated in Poul Anderson’s The High Crusade). Lewis’s friend J. R. R. Tolkien may have been an inspiration for this character.


Lewis’s naming of the planets. Out of the Silent Planet is set on Malacandra (Mars).

Lewis’s special interest was Mediaeval and Renaissance literature. In Out of the Silent Planet he is taking the cosmology of Dante’s great trilogy (see my discussion of the Inferno, Purgatorio, and Paradiso) and putting it through a Copernican Revolution, while retaining the Christian worldview. Naïve correspondences with Dante should be resisted, however, since Lewis was not originally intending to write a trilogy. If one absolutely must draw links, Out of the Silent Planet would probably correspond to the Purgatorio, with its emphasis on permissible vs wrongful desires.

Goodreads rates this ground-breaking novel 3.92. I’m giving it four and a half stars.

4.5 stars
Out of the Silent Planet by C. S. Lewis: 4½ stars


Fairy tale retellings


Little Red Riding Hood, as depicted by Gustave Doré (1883)

A few years ago, I blogged about fairy tales. “About once every hundred years some wiseacre gets up and tries to banish the fairy tale,” C.S. Lewis wrote in 1952, and Richard Dawkins had done exactly that.

Fairy tales are stories that have stood the test of time, and that means they have power. That power can be harnessed to teach science to children, but I don’t want to talk about that today; I want to talk about fairy tale retellings, which have become popular again in recent years.

It seems that Einstein did not say “If you want your children to be intelligent, read them fairy tales” – but fairy tales do develop the imagination and speak to the human heart. And retellings keep fairy tales fresh.

Fairy tales are generally classified as fantasy, and most retold fairy tales fall within that genre too. Among my favourites are the dream-like novels of Patricia A. McKillip, including In the Forests of Serre (2003), which incorporates Slavic tales of Baba Yaga and the Firebird. In fact, pretty much everything that Patricia A. McKillip has written is superb.


“This Mortal Mountain” (1967), a novelette by Roger_Zelazny, collected in The Doors of His Face, the Lamps of His Mouth (1971) and This Mortal Mountain (2009)

Fairy tales can be retold as science fiction too. After all, “any sufficiently advanced technology is indistinguishable from magic.” In “This Mortal Mountain” (1967), Roger Zelazny mashes together Sleeping Beauty (or “Doornroosje” as I first learned to call it) with Dante’s Purgatorio, in a story of mountain-climbing on a distant planet: “‘A forty-mile-high mountain,’ I finally said, ‘is not a mountain. It is a world all by itself, which some dumb deity forgot to throw into orbit.’ … I looked back at the gray and lavender slopes and followed them upward once more again, until all color drained away, until the silhouette was black and jagged and the top still nowhere in sight, until my eyes stung and burned behind their protective glasses; and I saw clouds bumping up against that invincible outline, like icebergs in the sky, and I heard the howling of the retreating winds which had essayed to measure its grandeur with swiftness and, of course, had failed.”

The spell described in this novelette is purely technological, but yet the story reduces me to tears every time I read it: “The planes of her pale, high cheeks, wide forehead, small chin corresponded in an unsettling fashion with certain simple theorems which comprise the geometry of my heart.”

The Lunar Chronicles, which I have not read, are a series of young adult science fiction fairy tale retellings, so the science fiction spin still exists.

Many fairy tales were originally intended to be scary. The terror of walking through a wolf-infested forest armed with, at most, a knife for protection is something that is difficult to imagine today, when Canis lupus is so much less common in the wild than it used to be. Deliberately swimming in shark-infested waters is perhaps the closest modern equivalent. Added to the wolves, bears, trolls, and giants, fairy tales also frequently have supernatural threats. In Faerie Tale (1988), Raymond E. Feist retells some Irish mythology as the straight horror it was perhaps once meant to be.

Fairy tales can also be retold with great success as Westerns. As with science fiction retellings, the frontier elements of danger and of the unknown help to set the scene. A particularly good example is The Mountain of the Wolf (2016), in which Elisabeth Grace Foley retells Little Red Riding Hood (or “Roodkapje” as I first learned to call it), but with a believable motivation for Red Riding Hood’s presence in the danger zone (I grew up with a Dutch children’s game that acted out the story; Red Riding Hood’s motivation in the original tale always struck me as confused).

Finally, fairy tales can be twisted. The outcome may be altered; the hero may become the villain; the beautiful dragon may be rescued from a ravening princess. This can become very dark, bordering on horror, or it may be light comic fantasy. And amusing recent example of the latter is The Reluctant Godfather (2017), a retelling of Cinderella by Allison Tebo in which the fairy godmother is (a) male and (b) totally uninterested in helping Cinderella out. In the movie world, Hoodwinked! is a well-known example of the twisted fairy tale in its comic form.

So there you have it. How do you take your fairy tales: black, or with cream and sugar?


Misquotes for Science

It’s a tough call, but the award for silliest statement at the March for Science has to go to the line “Dante said that the hottest places in Hell are reserved for those who remain neutral in times of moral crisis.” Dante never said anything of the sort, of course – the line is derived from something JFK said (“The hottest places in Hell are reserved for those who in time of moral crisis preserve their neutrality”), derived in turn from a chain of misquotes going back to Theodore Roosevelt. I’ve written before about Dante and Science, but suffice to say that in Dante’s Inferno, the worst regions are actually icy cold, and “neutrals” are not found there:

Please, let’s not have any “alternative facts” about Dante. The climate of the Inferno is important too.


Science in Dante’s “Paradiso”

In his Paradiso, which completes the trilogy begun with the Inferno, Dante travels through the (Ptolemaic) heavens, which look like this:

While most of Dante’s astronomy has been rendered obsolete by discoveries that began with Copernicus, Dante did understand the nature of the Milky Way. The Paradiso, it is true, expresses a degree of doubt regarding this:

As, graced with lesser and with larger lights
between the poles of the world, the Galaxy
gleams so that even sages are perplexed;
” — Paradiso, XIV, 97–99, tr. Mandelbaum

However, Dante’s Convivio provides the correct explanation:

In the Old Translation [Aristotle] says that the Galaxy is nothing but a multitude of fixed stars in that region, so small that we are unable to distinguish them from here below, though from them originates the appearance of that brightness which we call the Galaxy … Avicenna and Ptolemy seem to share this opinion with Aristotle.” — Convivio, II, 14, tr. Lansing


Milky Way; photo by “Eclipse.sx”

In the Paradiso, Dante discusses more than just theology and astronomy. He somehow manages to work in Thales’ theorem, for example (Paradiso, XIII, 101–102). What’s more, having told us in the Purgatorio (XV, 16–21) that “the angle of incidence is equal to the angle of reflection,” Dante now proposes an actual experiment in optics (no, it wasn’t Galileo who invented the experimental method!):

Yet an experiment, were you to try it,
could free you from your cavil – and the source
of your arts’ course springs from experiment
Taking three mirrors, place a pair of them
at equal distance from you; set the third
midway between those two, but farther back.
Then, turning toward them, at your back have placed
a light that kindles those three mirrors and
returns to you, reflected by them all.
Although the image in the farthest glass
will be of lesser size, there you will see
that it must match the brightness of the rest.
” — Paradiso, II, 94–105, tr. Mandelbaum

The image above (click to zoom) is the result of replicating Dante’s proposed experiment with the Persistence of Vision Raytracer. The unnecessary third mirror tells us that Dante is here also speaking allegorically about the reflection of Divine light, and that – hinting at 1 Corinthians 13:12 – he is looking forward to his final vision of the Trinity, in what is after all a theological poem:

That light supreme, within its fathomless
Clear substance, showed to me three spheres, which bare
Three hues distinct, and occupied one space;
The first mirrored the next, as though it were
Rainbow from rainbow, and the third seemed flame
Breathed equally from each of the first pair.
” — Paradiso, XXXIII, 115–120, tr. Sayers

See also science in the Inferno and in the Purgatorio.

Science in Dante’s “Purgatorio”

Dante’s Purgatory, described in the sequel to the Inferno, is a mountain in the South Pacific (the antipodes of Jerusalem). This painting by Agnolo Bronzino shows Dante gazing at the mountain:

Being in the Antipodes, the stars are naturally different, as all inhabitants of the Southern Hemisphere know:

Then I turned to the right, setting my mind
upon the other pole, and saw four stars
not seen before except by the first people.
Heaven appeared to revel in their flames:
O northern hemisphere, because you were
denied that sight, you are a widower!
” — Purgatorio, I, 22–27, tr. Mandelbaum

Dante has a nice description of time zones too (though with an average error of about two hours):

As when his earliest shaft of light assails
The city where his Maker shed His blood,
When Ebro lies beneath the lifted Scales
[i.e., midnight]
And noontide scorches down on Ganges’ flood,
So rode the sun; thus day was nightward winging
When there before us God’s glad angel stood.
” — Purgatorio, XXVII, 1–6, tr. Sayers

See also science in the Inferno and in the Paradiso.

Science in Dante’s “Inferno”

It is a common myth that the medievals thought that the world was flat. One of many proofs to the contrary is in Dante’s Inferno, written in the early 1300s. This poem depicts the standard medieval view of a spherical Earth – and, since the poem is set at Easter time, it’s appropriate to revisit it this month. In the poem, Dante actually travels down a Hell described as conical, through the centre of the Earth (long before Jules Verne!), and up into the Southern Hemisphere:

Dante correctly describes the shift in direction of gravity when passing through the centre of the Earth, and the effect of travelling to the Antipodes:

And he to me: You still believe you are
north of the center, where I grasped the hair
of the damned worm who pierces through the world.
And you were there as long as I descended;
but when I turned, that’s when you passed the point
to which, from every part, all weights are drawn.
And now you stand beneath the hemisphere
opposing that which cloaks the great dry lands
and underneath whose zenith died the Man
whose birth and life were sinless in this world.
” — Inferno, XXXIV, 106–115, tr. Mandelbaum

That is, by travelling through the centre of the Earth, Dante and Virgil arrive in the South Pacific, directly opposite Jerusalem, at about 32°S 145°W, around 460 km south of Rapa Iti.

Dante suggests here that the Southern Hemisphere is largely covered by water. There was an ancient belief in a Terra Australis, but Dante has rearranged geography so that the Southern Continent becomes a single, though extremely high, mountain. It was several centuries later that explorers like Abel Tasman and James Cook resolved the Terra Australis question.

See also science in the Purgatorio and in the Paradiso.