Looking back: 2001

The 1968 film 2001: A Space Odyssey suggested that we would have extensive space flight in 2001. That turned out not to be the case. What we did get was the September 11 attacks on the USA and the military conflicts which followed. Nevertheless, NASA commemorated the film with the 2001 Mars Odyssey orbiter.

Films of 2000 included the superb The Lord of the Rings: The Fellowship of the Ring, several good animated films (including Monsters, Inc., Shrek, and Hayao Miyazaki’s Spirited Away), the wonderful French film Amélie, some war movies (Enemy at the Gates was good, but Black Hawk Down distorted the book too much for my taste), the first Harry Potter movie, and an award-winning biographical film about the mathematician John Nash.

In books, Connie Willis published Passage, one of my favourite science fiction novels, while Ian Stewart explained some sophisticated mathematics simply in Flatterland.

Saul Kripke (belatedly) received the Rolf Schock Prize in Logic and Philosophy for his work on Kripke semantics, while Ole-Johan Dahl and Kristen Nygaard (also belatedly) received the Turing Award for their work on object-oriented programming languages (both these pioneers of computing died the following year).

The year 2001 also saw the completion of the Cathedral of Saint Gregory the Illuminator in Armenia, which I have sadly never visited.

In this series: 1978, 1980, 1982, 1984, 1987, 1989, 1991, 1994, 2000, 2001, 2004, 2006, 2009.


Cycles

The Tropical Year: 31.6888 nHz

One of the most important cycles we live by is the tropical year, measured from equinox to corresponding equinox (or solstice to corresponding solstice). The tropical year lasts, on average, 365.2422 days (365 days, 5 hours, 48 minutes, 45 seconds), which means that it is an oscillation with a frequency of 31.6888 nanohertz (nHz). This is the cycle of the seasons.

Spring, summer, autumn, and winter are the conventional seasons, but the tropical year may be split up into more than or less than four seasons, and these need not be of equal length. In northern Australia, a frequent division is “the dry” (May to September), “the build up” (September to December), and “the wet” (December to April). Local Aboriginal people, however, may recognise as many as six seasons.

The Sidereal Year: 31.6875 nHz

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the stars. This is the time that it takes for the sun to move through the “signs of the zodiac.” Because of the precession of the equinoxes, the sidereal year is 365.2564 days, which is about 20.4 minutes longer than the tropical year. As a result, ancient rules assigning dates to the signs of the zodiac are now completely wrong. The sidereal year corresponds to an oscillation of 31.6875 nanohertz.

The Synodic Month: 391.935 nHz

A synodic month is a cycle from new moon to new moon or full moon to full moon. This period actually varies by several hours, but it averages out to 29.530588 days (29 days, 12 hours, 44 minutes, 3 seconds).

In 432 BC, Meton of Athens noted that 235 synodic months (6939.7 days) is almost exactly equal to 19 years (6939.6 days). This period is called the Metonic cycle, and is used for predicting solilunar events such as the date of Easter.

The synodic month is also strangely similar to the average menstrual cycle (28 days), and this is reflected in the word (“menstrual” derives from the Latin mēnsis = month).

The Week: 1.65344 µHz

The week has an origin among the ancient Hebrews. It also has a Babylonian origin (the relationship between the two origins is unclear). The Babylonians related the 7 days of the week to the sun, moon, and 5 visible planets. They also related them to various gods. Our days of the week derive from the Babylonian week, via Greece and Rome: Sunday (Sun), Monday (Moon), Tuesday (Tiw, god of war = Mars), Wednesday (Woden = Mercury), Thursday (Thor = Jupiter), Friday (Frigg = Venus), and Saturday (Saturn).

Early Christians related the two week concepts together, pointing out that the day of the Resurrection (the day after the Jewish Sabbath) corresponded to the day of the Sun in the Roman system. The week corresponds to an oscillation of 1.65344 microherz.

The Sidereal Day: 11.6058 µHz

A sidereal day is the time that it takes the earth to rotate once around its axis. It often surprises people to discover that this time is 23 hours, 56 minutes, 4.1 seconds. It can be measured by the time to go from a star being overhead to the same star being overhead again.

The Solar Day: 11.5741 µHz

A solar day (24 hours, give or take some seconds) is the time from noon to noon. It is longer than a sidereal day because, while the earth is rotating around its axis, it is also moving around the sun. To put it another way, the sun is not a fixed reference point for the earth’s rotation. The difference between the sidereal and solar days mean that the stars seem to rise about 3 minutes and 56 seconds earlier every night.


Fast Fibonacci numbers

There was some discussion on reddit recently of the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584, 4,181, 6,765, 10,946, 17,711, 28,657, 46,368, 75,025, 121,393, 196,418, 317,811, 514,229, 832,040, …) and efficient ways of calculating them.

One way of doing so is using numbers of the form a + b σ where  σ is the square root of 5. Multiplication of such numbers satisfies:

(a + b σ) × (c + d σ) = ac + 5bd + (ad + bc) σ.

We can define the golden ratio φ = (1 + σ) / 2 and also ψ = 1 − φ = (1 − σ) / 2, in which case the nth Fibonacci number Fn will be exactly (φn − ψn) / σ. This is known as Binet’s formula.

We can use this formula to calculate Fibonacci numbers using only integer arithmetic, without ever evaluating the σ. We will have:

(2 φ)n − (2 ψ)n = (1 + σ)n − (1 − σ)n = 0 + p σ

for some integer p, and division by a power of two will give Fn = p / 2n.

I am using the R language, with the gmp package, which provides support for large integer matrices, and this allows us to use the relationship:

If we call this matrix A and calculate An−1, the first number in the resultant matrix will be the nth Fibonacci number Fn. The following R code calculates F10 = 55 using a combination of multiplication and squaring:

n <- 10

A <- matrix.bigz(c(
	1, 1,
	1, 0), 2)

p <- function(n) {
	if (n == 1) A
	else if (n %% 2 == 1) A %*% p(n-1)
	else {
		b <- p(n/2)
		b %*% b
	}
}

p(n-1)[1,1]

This same code will calculate, for example:

The time taken to calculate Fn is approximately proportional to n1.156, with the case of n = 1,000,000,000 (giving a number with 208,987,640 digits) taking about a minute.


Rods and cones in the human eye

I already posted these images (click to zoom) on Instagram. They illustrate the sensitivity to colour of the rods (lower right) and the three types of cones in the human eye. Cone sensitivity data is from CVRL.

Notice that red light is pretty much invisible to the rods. This is why red light does not interfere with night vision, and is used in e.g. this aircraft cockpit:


Greenhouse emissions in Australia

I thought I would take the opportunity today to talk about energy production and greenhouse gas emissions in Australia. The chart below shows the populations (blue bars) and population densities of the six Australian states plus the Northern Territory. Note that New South Wales, Victoria, and Queensland have the highest populations (8.2, 6.7, and 5.2 million respectively), while the Northern Territory has the lowest. However, given its smaller area, Victoria has the highest population density (29.4 people per sq km), while Western Australia and the Northern Territory have the lowest population densities (1.1 and 0.2 people per sq km respectively).

The next chart shows the per capita electricity production of the six Australian states and the Northern Territory, by type. These figures are adjusted for net electricity transfer between states. For example, Tasmania imports some mainland coal-fired power.

Notice that the totals are high in the less densely populated regions (Western Australia and the Northern Territory). The total is also high in Tasmania, because of the widespread use of hydro-electrically produced electricity for heating there.

Total per capita electricity production is lowest in Victoria, in part because of the widespread use of natural gas for heating and cooking (total gas use in Australia generally is about 4 times its use in electricity production). Victorian electricity is the dirtiest, however, with heavy use of brown-coal-fired production. Brown coal is by far the dirtiest fuel; it produces about 47% more greenhouse gases per MWh than black coal, and triple the greenhouse gases per MWh of natural gas.

South Australia has achieved 50% renewable energy, but this is not without its problems:

  • Wind and solar power are more expensive, so that South Australians pay about $360 per MWh for their electricity: 44% more than the two large states
  • The sun does not always shine and the wind does not always blow: this means that, in the absence of massive-scale energy storage, South Australia has to “borrow” coal-fired power from the East, although this is eventually repaid with interest
  • Solar and wind power cause substantial grid stability and grid synchronisation issues, which become very apparent at the 50% renewable level – good solutions are needed for this; South Australia currently copes by turning solar power off

To avoid “borrowing” electricity, massive-scale energy storage is required. South Australia would need several days worth of demand, at 40 GWh per day. Their famous Tesla battery has been expanded to a capacity of just 0.2 GWh, which is about a thousandth of what is needed. Batteries appear inadequate for energy storage at the required scale, and hydrogen storage is probably what we want.

Tasmania operates at a 92% renewable electricity level, thanks to multiple hydroelectric dams, which do not suffer from the problems of wind and solar (and availability is only an issue during lengthy droughts). In addition, hydroelectric dams can also provide energy storage for solar and wind power, simply by pumping water uphill. It is unfortunate that environmental groups in Tasmania have campaigned heavily against hydroelectric power.

The last chart shows the per capita CO2-equivalent emissions for state electricity generation, plus other emissions (including agriculture, other energy use, industrial processes, waste, forestry, and land use change). Agricultural emissions are highlighted in green. A note of caution, however: the electricity generation data is for 2019, but the total greenhouse emissions are for 2018 (the latest I could find). These numbers cannot be compared to those of other countries, unless the numbers for other countries are equally recent and also include the full range of emissions, per UNFCCC standards (some comparable national averages are shown on the left).

Note that net greenhouse emissions for Tasmania are negative, largely due to tree-planting. Per capita emissions for the large, less densely populated areas are higher than those for New South Wales and Victoria; in part due to transportation requirements (shifting commuters and freight from road to rail would help here). Agricultural emissions per capita are particularly high in the Northern Territory, because the impact of cattle farming is being divided among a tiny population of just 0.2 million people. The overall Australian average of 21.2 tonnes per capita is quite significantly affected by the inevitably high emissions for the large, less densely populated areas. There is also the question of whether emissions due to mining and agriculture should be attributed to the producing country, or to the country of final consumption.

Economically and geographically, Australia is in many ways more like a Central Asian country than a European one, given its large size and its heavy reliance on mining and agriculture (Australia’s greenhouse emissions are comparable to those of Kazakhstan, which produces 21.7 tonnes per capita). However, progress could be made in Australia with more energy-efficient housing and transportation.

It should also be emphasised that, given its small population, Australia’s greenhouse emissions make a neglible contribution to the global and regional climate. If increasing atmospheric CO2 has an effect in Australia’s region, that is due primarily to emissions by the large countries of the world, particularly China (which produces about a third of the world’s CO2). Australia should, no doubt, reduce its greenhouse emissions, but whether Australia does so or not will make no measurable difference to the global or regional climate.


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


Personality Types and Social Media

Following some discussion with friends, I made a chart comparing the general prevalence of MBTI personality types with their prevalence on Facebook (using data from this report). The first of each pair of bars is general prevalence, and the second is prevalence on Facebook.

It can be seen that extroverted types are more likely to be on Facebook than introverted types. However, the IN-J types swim against the tide. The chart below provides a bit of a summary.

The third chart shows the results for Twitter. Here extroverts are also over-represented, especially the EN-P and ESTJ types, but not the other ES– types. Among the introverts, the ISTJ type swims against the type, and is in fact the most common personality type on Twitter.


Houston, we have a problem

Some years ago, I posted the chart above, inspired by a classic XKCD cartoon. The infographic above shows the year of publication and of setting for several novels, plays, and films.

They fall into four groups. The top (white) section is literature set in our future. The upper grey section contains obsolete predictions – literature (like the book 1984) set in the future when it was written, but now set in our past. The centre grey section contains what XKCD calls “former period pieces” – literature (like Shakespeare’s Richard III) set in the past, but written closer to the setting than to our day. He points out that modern audiences may not realise “which parts were supposed to sound old.” The lower grey section contains literature (like Ivanhoe) set in the more distant past.

The movie Apollo 13 has now joined the “former period piece” category. Released in 1995, it described an event of 1970, 25 years in the past. But the ill-fated Apollo 13 mission of 11–17 April 1970 is now 51 years in the past; the movie is closer to the event than it is to us (although the phrase “Houston, we have a problem” – in real life, “Houston, we’ve had a problem” – has become part of the English language).

The image shows the real-life Apollo 13 Service Module, crippled by an explosion (left), together with a poster for the 1995 movie (right). Maybe it’s time to watch it again?


Planet Narnia: a book review


Planet Narnia: The Seven Heavens in the Imagination of C. S. Lewis (2008) by Michael Ward

More than a decade ago, on a blog that no longer exists, I reviewed Planet Narnia: The Seven Heavens in the Imagination of C. S. Lewis by Michael Ward (written a few years before Ward converted to Catholicism). Ward’s thesis was that C. S. Lewis wrote The Chronicles of Narnia based on a secret plan linking the seven novels to the seven classical planets (Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn). This plan was allegedly so secret that Lewis shared it with none of his friends.

People are still reading Planet Narnia, so it’s worthwhile re-stating my opinions, especially since I’ve done some recent analyses that are relevant.

While Ward’s book has been widely praised, not everybody has agreed with his thesis. In an interview, Lewis’s stepson Douglas Gresham stated, “A very nice man and a friend of mine, Michael Ward, has recently written and published a book all about how the Narnian Chronicles are all based on the seven planets of the medieval astronomical system. I like Michael enormously, but I think his book is nonsense.

Devin Brown is one scholar who is critical. Brenton Dickieson is another. In fact, in a letter to a child, Lewis himself is quite clear that there was no plan: “The series was not planned beforehand as she thinks. When I wrote The Lion I did not know I was going to write any more. Then I wrote P. Caspian as a sequel and still didn’t think there would be any more, and when I had done The Voyage I felt quite sure it would be the last, but I found I was wrong.

There is something terribly seductive about correspondence theories like Ward’s. Plato, for example, argued that the atoms of the “four elements” (Earth, Air, Fire, and Water) corresponded to four of the Platonic Solids. Earth atoms were cubes, because cubes can be stacked to form shapes. Water atoms were icosahedra, because water flows and icosahedra are the roundest of the Platonic Solids. Fire atoms were tetrahedra, because fire burns, and that’s obviously a result of the sharp points on fire atoms. And by now we’re basically just assuming the hypothesis, so we simply state that air atoms are octahedra. Plato was a great philosopher, but that isn’t how reasoning is supposed to work.

In a similar vein to Justin Barrett’s “Some Planets in Narnia: A Quantitative Investigation of the Planet Narnia Thesis” (Seven, vol. 27, Jan 2010), I have explored the frequencies of 20 words or word groups associated with the seven planets (I allow for variations in word endings). The 20 bar charts show the frequencies, adjusted for the total word count of each book (but the small white numbers show actual counts). The bars list the seven Narnia books in order of internal chronology (i.e. The Magician’s Nephew first). The stars mark the book that Michael Ward thinks is associated with the relevant planet; the star is black if the relevant bar is indeed the highest.

One might add the exclamation “By Jove!,” which occurs only twice in the supposedly “Jovial” The Lion, the Witch and the Wardrobe, but 5 times in Prince Caspian and 4 times in The Silver Chair. Looking at the chart, we start well with two “hits” linking the Sun with The Voyage of the Dawn Treader, but then there are only four more hits (and most of those can be explained purely on the basis of plot). All up, 6 hits out of 20, when we would have expected 20/7, or just under 3. This is not statistically significant.

It is also worth noting that we know how Lewis wrote when he was making connections to the planets. For example, Lewis’s Perelandra is based on Venus, and Lewis throws in 7 references to the metal associated with her: “coppery” (3×), “copper-coloured” (3×), and “coppery-green” (1×). There are no such references in Out of the Silent Planet, and just one in That Hideous Strength (and that is in a reference to Venus: “I have long known that this house is deeply under her influence. There is even copper in the soil. Also – the earth-Venus will be specially active here at present.”). However, there is only one mention of copper in The Magician’s Nephew, which Ward claims is also linked to Venus (“The feathers shone chestnut colour and copper colour.”). That is to say, an important Lewisian reference to Venus is not present in any significant way in The Magician’s Nephew.

Now Ward gets around these and other problems by claiming that Lewis didn’t always follow the plan: “Nevertheless, for all its apparent ungraciousness, we can bear in mind that Lewis was unlikely to have been perfectly successful in carrying out his own plan” (p. 233). But if Lewis didn’t follow the plan, one questions what kind of “plan” it was.


Hope, Love, and Faith (photo: Anthony Dekker)

In his story “The Honour of Israel Gow,” G. K. Chesterton writes: “I only suggested that because you said one could not plausibly connect snuff with clockwork or candles with bright stones. Ten false philosophies will fit the universe; ten false theories will fit Glengyle Castle. But we want the real explanation of the castle and the universe.” In that spirit, I offer an alternate theory (the core of which was developed collaboratively) which I also blogged about more than a decade ago. Not that I think that my theory is necessarily right, just that it’s a better theory than Ward’s, and therefore casts doubt on his proposal. A theory should, after all, explain the facts better than any alternative theory.

And my theory is this: that the seven Narnia stories are linked to the Seven Virtues: Love, Faith, Hope, Prudence, Temperance, Fortitude, and Justice. This fits what we know about composition. Of course, if you thought you were writing just one Christian children’s book, it would be about Love. Of course the next two books written would be about Faith and Hope. Of course the four “cardinal virtues” would come last. So how does this work?

I get 11 “hits.” That’s 11 out of 25, because I discarded 5 options while producing the chart, but the match is still extremely significant, with p < 0.04%. Shields are a common Christian symbol of Faith (Ephesians 6:16) and they are mentioned especially often in Prince Caspian, which I associate with that virtue (and see also the line “We don’t forget. I believe in the High King Peter and the rest that reigned at Cair Paravel, as firmly as I believe in Aslan himself.”).

Anchors are a common Christian symbol of Hope (Hebrews 6:19) and they are mentioned especially often in The Voyage of the Dawn Treader (and see also “But Reepicheep here has an even higher hope… I expect to find Aslan’s own country. It is always from the east, across the sea, that the great Lion comes to us.”). The Horse and His Boy is full of bravery in the face of fear, i.e. of Fortitude (e.g. “And now at last, brave girl though she was, her heart quailed. Supposing the others weren’t there! Supposing the ghouls were! But she stuck out her chin (and a little bit of her tongue too) and went straight towards them.”).

The Silver Chair has Puddleglum to demonstrate Prudence, and the final judgement in The Last Battle demonstrates Justice. It is really only for The Magician’s Nephew that I have failed to make my case, but there one can take Uncle Andrew and Jadis as examples of the absence of Temperance (as in “… he thinks he can do anything he likes to get anything he wants.”).


Hope and anchors have a long association. This flag was embroidered by Jane, Lady Franklin for one of many expeditions searching for her lost husband (photo credit)

To quote Chesterton again: “Ten false philosophies will fit the universe; ten false theories will fit Glengyle Castle.” Another theory for the Narnia books that has been suggested to me is that they correspond to the seven liberal arts, with the first three books written corresponding to the Trivium (Grammar, Logic, and Rhetoric, in that order) and the last four books written corresponding to the Quadrivium (Arithmetic, Geometry, Music, and Astronomy).

We can count words as before, except that the category “long words” (corresponding to Rhetoric) includes all words of 11 or more letters, such as “crestfallen,” “unmitigated,” or “waterspouts.” We get 8 “hits” this way (2 more than for Ward’s theory). Allowing for discarded options, this is statistically significant, with p < 2%. The pairings of The Lion, the Witch and the Wardrobe with Grammar and Prince Caspian with Logic are rather unconvincing, but I think that this theory is still better than that of Michael Ward.

One can even find characteristic colours in the books, with the words “green,” “white,” “blue,” and “black” occurring particularly often in The Magician’s Nephew (52), The Lion, the Witch and the Wardrobe (59), The Voyage of the Dawn Treader (26), and The Silver Chair (39), respectively.

Chesterton (or, rather, Father Brown) concludes with what is really the fundamental principle of science: “But we want the real explanation of the castle and the universe.” And I don’t think that Michael Ward has the real explanation of the Narnia books. Indeed, even if one assumes that the Narnia stories follow a plan, there are better candidates for a plan than the one that Ward suggests.

Goodreads rates Planet Narnia 4.3 out of 5, because (judging by the comments) people largely seem to believe Ward’s argument, which I find so unconvincing. However, I can really only give his book two stars:

* *
Planet Narnia by Michael Ward: 2 stars