Mathematical metaphors

Mathematics is, by its very nature, as disjoint from reality as is chess. But now and then some mathematical result can be interpreted in such a way that, in a receptive eye, it reflects some aspect of reality. Below, we consider some of these mathematical metaphors. 'Meta-phor' means 'to carry over' and this is exactly what happens.

Plutarch. De Iside et Osiride, section 56 (online here):

Now in that triangle the perpendicular consists of three parts, the base of four, and the subtense of five, its square being equal in value with the squares of the two that contain it. We are therefore to take the perpendicular to represent the male property, the base the female, and the subtense that which is produced by them both. We are likewise to look upon Osiris as the first cause, Isis as the faculty of reception, and Horus as the effect. For the number three is the first odd and perfect number, and the number four is a square, having for its side the even number two. The number five also in some respects resembles the father and in some again the mother, being made up of three and two.

 Guido Grandi. In 1703, Grandi published Quadratura circuli et hyperbolae (online here), concerning which we learn from Grandi's biography (here) the following:

One of Grandi's results in the Quadratura caused a lot of interest. He used the series expansion

¹/_1+x = 1 - x + x² - x³ + x⁴ - ...

and putting x = 1, obtained 1 - 1 + 1 - 1 + 1 - 1 + ... = ¹/₂. However, he argued that (1 - 1) + (1 - 1) + (1 - 1) + ... = 0 + 0 + 0 + 0 +... . In the first draft of the work, Grandi claimed that since the sum of infinitely many 0s equaled ¹/₂ he had proved that God could create the word out of nothing. The censor allowed the mathematics to be published but required the removal of the comment that it showed God could create the word out of nothing. Grandi reluctantly agreed to remove the comment but many mathematicians across Europe discussed Grandi's result that 0 + 0 + 0 + 0 +... = ¹/₂.

The series, in geometrical form, is to be found on page 51 of Quadratura (Corollarium III to Propositio VII). Grandi complied with the censor, but defended himself vigorously in Riposta apologetica (1712, online here). The discussion concerning the challenged interpretation starts on page 153. The core of the mathematico-theological debate is the principle ex nihilo nihil: out of nothing you get nothing (p.157).

Back to the metaphor: Grandi viewed his 'equation' (which is mathematical nonsense according to today's standards)

0 + 0 + 0 + 0 +... = ¹/₂

as a symbol of 'Creation out of nothing'.

Kepler. In May 1608, Kepler wrote a letter to Joachim Tancke (Latin original here, English translation of the relevant passage here) in which he dwells on the "divine proportion". As always with Kepler, it's a mix of mysticism and science. Even so, the content is very interesting, because, for the first time in history, the golden and/or Fibonacci numbers are somehow linked to the physical world.

We start with five properties concerning the golden and Fibonacci numbers of which Kepler seems to have been (qualitatively) aware in writing the letter.

The first one is trivial, given that a/b=b/(a+b) is the geometrical definition of the golden section, and the subsequent equalities just repeat that definition. For (2): algebraically, φ is the irrational number (√5-1)/2. Properties (3) and (4) are in fact basic properties of convergents of continued fractions, applied to φ.  For a direct proof of (4) see e.g. ProofWiki, Cassini's Identity. Formula (5) is the case m-1=n of ProofWiki, Fibonacci Number in terms of smaller Fibonacci Numbers.

For Kepler, the divine proportion is the "model of (pro)creation", archetypus generationis, and he gives several reasons for this.

(a) what was formerly the larger part now becomes the smaller, what was formerly the whole now becomes the larger part, and the sum of these two now has the ratio of the whole. This goes on indefinitely; the divine proportion always remaining. I believe that this geometrical proportion served as idea to the Creator when He introduced the creation of likeness out of likeness, which also continues indefinitely. 

This is a theological interpretation of property (1) above, and far from convincing. The A4-format, with ratio √2:1, can be described in much the same way: folding it in half, the smaller dimension becomes the larger dimension of the next generation, the ratio remaining, and this too goes on indefinitely.

(b) I see the number five in almost all blossoms which lead the way for a fruit, that is, for creation;  and the number five, that is the pentagon, is constructed by means of the divine proportion.

This botanical observation (even extended to Fibonacci numbers in general) is by no means a general rule. Moreover, the presence of 5 in nature need not be the result of the golden ratio mysteriously at work, no more so than that a four-petaled flower is the trace of √2 or a circular flower head reveals the presence of π.

(c) there exists between the movement of the earth and that of Venus, which stands at the head of generative capability, the ratio of 8 to 13 which comes very close to the divine proportion. 

The astronomical fact is (approximately) true: Venus orbits the sun in 224.7 days, the earth in 365.24, and the quotient is 0.61521... while 8/13=0.61538... (though φ=0.61803...). Astronomically, this is a "coincidental near ratio of mean motion". (Here you can read more about it, and about the many simple ratios of integers that result from perfect orbital resonance.) Kepler, as much an astrolo-gist as an astrono-mer, identifies the second planet from the sun with the eponymous goddess of love and fertility, and this makes further comments superfluous.

(d) the earth-sphere is midway between the spheres Mars and Venus. One obtains the proportion between them from the dodecahedron and the icosahedron, which in geometry are both derivatives of the divine proportion; it is on our earth, however, that the act of procreation takes place.

Here, the astronomical references to the dodecahedron and the icosahedron are irrelevant, because Kepler's model of the solar system (based on the medieval idea "because we know six planets, there are six planets") was completely wrong. Even the astrology involved seems very twisted, as it deduces some property of "the planet of procreation" from the two neighbouring planets.

 (e) the image of man and woman results from the divine proportion.  

Kepler rediscovers, in his own way, the sequence of Fibonacci numbers

1,1,2,3,5,8,13,21,...

with the peculiarity that the two numbers 1 must be considered as different, viz. as the minor and the major part of the number 2 decomposed. Strange, but let's read on. He emphasizes the properties (2) and (3) stated above, which have in fact nothing very special and could be adapted (with a different sequence of integers) for any irrational number. Leaving aside the first 1, the Fibonacci numbers are said to be alternatively male and female. The argument is as follows. If you consider any Fibonacci number, its square will be 1 more or 1 less than the product of its two neighbours (the preceding and the following one); see property (4) for the correct formula. Now a "square +1" is a square with a surplus (like a body with a penis) while a "square -1" is a square with a cavity (like a body with a vulva). When the two copulate, a new Fibonacci number results; this is our formula (5) above. Don't forget to add 1 to the one square (resulting in a male) while subtracting it from the other square (resulting in a female).

To make things perfectly clear, Kepler adds a diagram showing how the Fibonacci numbers 3 and 5 copulate and produce the Fibonacci number 34 as their offspring.

As for the sexes involved: 3 is "male" (Fibonacci neighbours 2 and 5, product 10, a square +1), while 5 is "female" (neighbours 3 and 8, product 24, a square -1). Kepler writes of these illustrations: observe that you clearly see a penis here and a vulva there. When they copulate (illustration at the bottom) the surplus 1 of the one square fills the defect 1 of the other square, here resulting in the Fibonacci number 34. (Note that, while the parents in the formula are approximate squares, the offspring is just the plain number; moreover, being odd-indexed, it will always be the same Keplerian gender.) We almost have two divine proportions Kepler writes. In fact, we almost have two golden rectangles: in the first case a 2x5 rectangle of 10 squares, in the second case a 3x8 rectangle of 24 squares.

In this mix of math and myth, (e) is clearly a metaphor because human bodies don't look like squares at all. On the other hand, (b) and (c) are scientific observations, one qualitative and one quantitative. In connecting golden and Fibonacci numbers and rectangles to physical reality, Kepler is 250 years ahead of Zeising. But, unlike Zeising, Kepler leaves (human) art alone, and is well aware of the distance separating maths and reality: 

I also play with symbols; I have started a small work: "Geometrical Cabbala"; it deals with the ideas of the things of nature in geometry. Only I play in such a way as to never forget that I am playing. For nothing is proven with symbols; in the philosophy of nature no secrets are unveiled by geometrical symbols.

 Herz-Fischler (A Mathematical History of the Golden Number, Dover 1998, p. 171) writes 

Even in Kepler's case the statements glorifying the DEMR [division in extreme and mean ratio] are always related to the mathematical properties.

Are they? We fail to see any mathematical reference in Kepler's statement, under (c), about the golden ratio orbits.

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A wicked combination: Zeising - Ghyka - Le Corbusier

References are to the pages of

• [C] Jean-Louis Cohen, Le Corbusier's Modulor and the Debate on Proportion in France, Architectural Histories 2(1) (2014), Article 23, pp. 1-14. [Contains also the original French texts of our English quotations.] (here)
• [M] Matila Ghyka, The geometry of art and life, Dover 1977 (original 1946). (here)
• [Z] Frank Zöllner, Anthropomorphism: From Vitruvius to Neufert, from Human Measurement to the Module of Fascism, In: K. Wagner and J. Cepl (editors): Images of the body in architecture. Anthropology and built space. Tübingen, Berlin 2014, pp. 47-75. (here)

 

Adolf Zeising (1810-1876) — Matila Ghyka (1881-1965) — Le Corbusier (1887-1965)

As explained here, Zeising invented Golden Numberism in 1854. Among those responsible for spreading this weird belief, two names must be mentioned expressly: the Romanian diplomat Matila Ghyka and the influential Swiss painter and architect who operated under the pseudonym Le Corbusier. 

Among Ghyka's many publications, we mention two that Le Corbusier owned:

•  Esthétique des proportions dans la nature et dans les arts (Aesthetics of Proportions in Nature and the Arts, a title which could have been Zeising's), 1927
• Le nombre d'or — rites et rythmes pythagoriciens dans le développement de la civilisation occidentale (The golden section — Pythagorean rites and rhythms in the development of western civilization), 1931

Ghyka recombined much of his writings into different forms, and The geometry of art and life (1946) offers a good English synthesis.

It is very clear that Ghyka believed everything Zeising had put forward. He mentions  

the dominant role of the golden section in the proportions of the human body, rediscovered [after the Greeks, that is] by Zeysing [sic], who also recognized its importance in the morphology of the animal world in general, in botany, in Greek architecture (Parthenon) and in music. [G16] 

As for the Parthenon, he writes that  

Zeysing already had observed the obvious presence of the Golden Section in the frontal view of the Parthenon [G124]. 

Actually, far from being obvious, the Golden Section is not present at all in the Parthenon and Zeising simply doesn't know how to deal with measurements. But for Ghyka, it's a simple fact that 

Zeysing had already noticed that Φ was the fundamental ratio for this façade [G136].

Also, he summarizes Fechner's biased experiment by stating that the golden rectangle obtained the great majority of votes [G10]. Actually, as explained here, an overwhelming 2/3 majority did not choose it.

The influence of Ghyka would have remained restricted had he not raised the interest of Le Corbusier. The latter became an internationally acclaimed architect, therefore seen by the general public as a solid scientific mind. Alas, if only this were true! He knew and admired Ghyka's writings, and described them as some esoteric revelation, in these very words:

a book of the revelations of the laws of our being and our world [C3]

of a nature so noble and so inaccessible that it requires much work and a certain intellectual persistence on behalf of those who seek the truth [C3]

deep enough to give you the key of the world [C11].

The laws of our being, the key of the world, no less! And yes, here comes the classic humbug with some esoteric flavour added:

The 'divina proportione' appears in mathematical relationships that are one and all, in whole and in part, in the facts and in the hypotheses, in the calculation, in geometry, in natural objects and in the paintings and architecture of major epochs (the Egyptians, Greeks, the Gothic, the Renaissance, French classicism etc.) [C11]

He also wrote 

It has been proved—particularly during the Renaissance— that the human body follows the golden rule. [Modulor 1, Chapter 2, p.56 (French original here)]

No doubt, Le Corbusier had completely wrong convictions about the golden ratio and the human body. Before Zeising (1854) no one ever saw any golden proportions in any body! Clearly, an architect guided by such wrong convictions must feel challenged to invent some golden standard worthy of such a supposedly great tradition. It was eventually born in 1948, and called the Modulor. The name is composed of the French words Module and Or ("gold", after "golden section"). Le Corbusier himself provides some insight into its genesis.

Ill luck so had it that almost all these metric values were practically untranslatable into feet and inches. Yet the 'Modulor' would, one day, claim to be the means of unification for manufactured articles in all countries. It was therefore necessary to find whole values in feet and inches. 

I had never anticipated having to round off certain figures of our two series, the red and the blue. One day when we were working together, absorbed in the search for a solution, one of us—Py— [Marcel Py] said: 'The values of the "Modulor" in its present form are determined by the body of a man 1·75 m. in height. But isn't that rather a French height? Have you never noticed that in English detective novels, the good-looking men, such as the policemen, are always six feet tall?' 

We tried to apply this standard: six feet=6 x 30·48=182·88 cm. To our delight, the graduations of a new 'Modulor', based on a man six feet tall, translated themselves before our eyes into round figures in feet and inches!  [Modulor 1, Chapter 2, p.56 (French original here)]

The ridiculous reference to good-looking policemen in detective novels convincingly proves the completely arbitrary nature of the "universal" norm invented by Le Corbusier. François Le Lionnais, mathematician and personal friend of Le Corbusier's, seemed to have been among the few men brave enough to challenge the invention. Le Corbusier was fair enough to include the criticism in the sequel Modulor 2 (1955). 

In order to remain within the modesty of our search, let us quote the following letter from Le Lionnais, mathematician and man of high culture:
 

Paris, 12th February, 1951


". . . As you know, I reproach certain authors—of whom, let me hasten to say, you are not one—with using the Golden Mean in a way which presupposes and encourages a point of view more or less akin to occultism. Every time the Golden Mean is mentioned, I feel it is necessary to define one's personal attitude on this point. But I need not pursue the matter further, for in this matter our points of view are the same. 

So far as the technical aspect is concerned, I believe that the Golden Mean does not represent a particularly exceptional or privileged concept; but it may repre­sent a useful convention and, as often happens, the adoption of a convention­—however arbitrary it may be—can lead to substantial progress, provided one remains faithful to it, because it becomes a principle of selection and order. Alpha­betical order, which does not rest on any natural foundation, is extremely useful and it would be foolish to criticize it. I have, of course, indulged in the mathe­matician's vice of "going to the extreme" in giving you an example which exaggerates my thought in order to make it more readily understandable. It is obvious that, whilst the Modulor has not the unique nature which would authorize it to impose a sort of dictatorship in the plastic arts, it nonetheless possesses certain natural characteristics which recommend it, with other numbers, to the attention of the artist and the technician."

Such is the mathematician's warning. [Modulor 2, Chapter 1, p.18-19 (French original here)]

Perhaps Le Lionnais was unaware of the esoteric ideas which Le Corbusier had copied from Ghyka. But, if he said they agreed on rejecting these, he may also have done so for friendship's sake. But he's very outspoken in calling the Modulor an arbitrary convention and the Golden Mean a concept without particular merits. (In 1983 Le Lionnais, in his book Les Nombres Remarquables, would himself make several wrong claims about the golden number, e.g., that the Greeks had made it the cornerstone of their aesthetic system. Relevant page here.)

It's is a very famous icon though, and we feel obliged to include it here. We do so reluctantly because it is not only based on wrong and arbitrary assumptions, it is at the same time very ugly. Remembering da Vinci's masterly composition of the Vitruvian Man, one feels embarrassed by Le Corbusier's clumsy drawing of a beefy man (apparently in a football pauldron, seen his shoulders) with a thin head and an oversized hand, standing in a vulgar position with one arm ambiguously stretched in a crooked fashion. The only body element unambiguously marked is the Zeisingian navel, the axiom on which the whole shaky construction rests.

 Famous icon of a wrong cause, yes, but there is also good news.  

As is well known, the golden section leads to irrational number relationships, which are hardly suited to architectural practice. Hence, the golden section was rarely used in architecture. [Z59]

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Marisha Pessl — Calamiteitenleer voor gevorderden

In 2004 verscheen Special Topics in Calamity Physics, de literaire eersteling van Marisha Pessl (geboren 1977). De Nederlandse vertaling is van 2006. Ik heb het boek nu voor de derde keer gelezen, en was er opnieuw helemaal door meegesleept, wat ook de kritiek mag zijn die ik erop heb.

Drammatis personae

(WAARSCHUWING! vol met spoilers)

1. Linkse terreurgroep ‘De Nachtwakers’

George Gracey, alias ‘Nero’. Geboren op 12 februari 1944 in Athene, Amerikaanse vader, Griekse moeder (p.515). Vermoordt op 9 juli 1971 (p.469) in Meade, West-Virginia, senator Michael McCullough, oom van Smoke Harvey. Hinkt. Woont op het Griekse eiland Paxos. Doet zich voor als Sorbonne-professor in de klassieke Griekse literatuur Michel Servo Kouropoulos (‘Baba au rhum’), stelt een kortstondig gehuurd appartement als zijn verblijf voor.

Catherine Baker, alias ‘De Mot’, geboren 1960. Dochter van oliemagnaat. Schoolvriendin van Natasha Bridges. Loopt op 13-jarige leeftijd van huis weg om Gracey te volgen. Vermoordt in september 1987 in Vallermo (later vervormd opgevangen als ‘Valerio’) een politieman (p.474). Doet zich voor als Hannah Louise Schneider, maar heeft die persoonlijkheid overgenomen van een weeskind uit New Jersey. Sinds drie jaar lerares ‘Filmkunde’ in Stockton. Camoufleert haar politieke contacten als rendez-vous in motels. Sterft op vrijdag 26 maart 2004 (p.335) door moord of zelfmoord. (Zie verder bij * voor een mogelijk scenario.) In 1992 (dood van Natasha Bridges) vriendin van Gareth Van Meer. Psychologisch verward. Heeft rond zich een kring van 16- tot 18-jarige leerlingen-bewonderaars, waaraan Blue als ‘eregast’ toegevoegd wordt (p.90).

Gareth Van Meer, alias ‘Socrates’, geboren in Biel (Zwitserland) op 25 juli 1947. Professor politicologie, ideoloog van de Nachtwakers. Rondreizend bestaan met veel korte verblijven dient als dekmantel voor contacten en recruteringen. Strijkt in 2003 neer in Stockton waar Hannah woont. Verdwijnt plotseling en definitief, nadat Blue hem geconfronteerd had met wat zij al wist. Laat geldmiddelen voor zijn dochter achter. Had de avond voordien de titel ‘Calamiteitenleer voor gevorderden’ gesuggereerd.

Andreo Verduga, Peruaanse tuinman bij Van Meer in Stockton. Verdwijnt spoorloos uit het ziekenhuis na een schotwond te hebben opgelopen. Misschien verbonden met Hannah en Gareth, en dus met de Nachtwakers (Brighella-kostuum, Howard, Wall-Mart, Hannahs slaapkamer, p.527). 

2. Andere personages.

Natasha Alicia Bridges, geboren in 1960, vrouw van Gareth, moeder van Blue. Bestudeert en verzamelt vlinders. Schoolvriendin van Hannah/Catherine. Verongelukt op 17 juli 1992, mogelijk zelfmoord.

Blue Van Meer, geboren 18 juni 1987 (p. 23, 512), 1m55 lang. Scherpzinnige dochter van Gareth en Natasha. Studeert glansrijk af in Stockton (schooljaar 2003-2004) en verhuist naar Harvard, waar zij haar Calamiteitenleer schrijft bij wijze van therapie. [Terzijde: de schrijfster heeft een dochter genaamd Avalon Blue, geboren lang nà het boek.]

Smoke Wyannoch Harvey, 'Dubs', 68 jaar, ex-bankier, schrijver, vastbesloten de moordenaar(s) van zijn oom senator McCullough te vinden. Verdrinkt in het zwembad van Hannah, misschien door de stille samenwerking van vele Nachtwakers.

Ada Shirley Harvey, dochter van Smoke. Zet diens speurwerk voort en speelt alles door aan Blue.

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Het boek speelt zich af in het schooljaar 2003-2004, aan een middelbare school in het Amerikaanse Stockton.

Elk hoofdstuk heeft als titel de naam van een boek of film. Vele daarvan kende ik niet, en ik heb niet de moeite gedaan om na te trekken wat het verband zou kunnen zijn tussen het hoofdstuk en de titel. Na enkele hoofdstukken sloeg ik de titel gewoon over.

Het boek wordt geschreven door de hoofdfiguur, Blue Van Meer, bij wijze van therapie om te herstellen van haar trauma's (twee doden en de onverklaarde verdwijning van haar vader) die ook haar geheugen verstoren. (De ingelaste tekeningen, die gedeeltelijk BVM weerspiegelen —soms zelfs letterlijk—, passen ook in die therapie.) BVM kan dus, al dan niet opzettelijk, de waarheid onjuist weergeven. Ook de schrijfstijl is de hare. Dit maakt het moeilijk om te weten welke kritiek men als lezer aan de schrijfster moet adresseren, en welke aan BVM, en welke fouten aan wie toe te schrijven zijn. De schrijfster kan op alles antwoorden dat niet zij aan het woord is, maar BVM.

Het boek bevat ontstellend veel erudiete verwijzingen, waarvan vele mij onbekend en allicht fictief zijn, en krioelt verder van de zeer kromme of vergezochte vergelijkingen. Blue’s klasgenoten (17 of 18 jaar oud, zijzelf is 16) zijn zeer blasé: hebben een eigen auto, lopen rond met een heupflacon whisky, chique outfit, roken sigaren, maken cocktails en werken in baancafés vluggertjes met truckers af. Dit is voor Europese normen nogal vreemd, maar onmogelijk is het niet. Maar wat niét kan: zij vuren constant spitse one-liners af die de doorsnee Amerikaan (laat staan puber) niet eens zou begrijpen. Die moet het literaire wonderkind BVM dus in de mond van haar personages gelegd hebben. Vreemde school ook, waar het aanbod reikt van ‘filmkunde’ (wat dat ook mag zijn) tot de snarentheorie uit de hedendaagse onderzoeksfysica.

Van de eerste tot de laatste bladzijde liggen in het boek faits-divers verstrooid die men geacht wordt uiteindelijk zelf tot een samenhangend verhaal te monteren. Iedereen krijgt zijn aandeel in ‘verdachte’ uitspraken en handelingen. Een ‘oplossing’ wordt niet verstrekt. Ik heb het boek nu drie keer gelezen en weet nog steeds niet welke van de tientallen mogelijke verklaringen de ‘juiste’ is. Het is misschien een ouderwetse opvatting, maar ik vind niet dat ik het werk van de schrijfster moet overnemen. Bovendien is ze zo onfair om mij essentiële informatie te onthouden. Iemand die zichzelf aan een boom ophangt heeft een steun nodig (de klassieke stoel), en de elementaire informatie over al dan niet een weggeschopte boomstronk wordt eenvoudigweg door de ooggetuige BVM of door de politie niet verstrekt. Evenmin wordt bevestigd dat de rondzwervende verdwaalde kampeerder met de bril inderdaad verklaard heeft dat hij het was die Hannah en BVM gadesloeg. Veel vragen waar BVM (en de lezer) blijft mee zitten zouden door de politie snel beantwoord worden. Ze zouden het ongetwijfeld de moeite waard vinden om na te trekken of diegene die onder een valse naam een luxe-residentie in Parijs gehuurd heeft inderdaad de leider van een terroristengroepering is. En niemand verdwijnt 's morgens vroeg uit een stil provinciestadje zonder ergens (door taxichauffeur, bij tankstation,...) opgemerkt te zijn. Veel puzzelstukken ontbreken dus, en andere passen slecht ineen. Misschien moet er met dobbelstenen gegooid worden; BVM maakt tenslotte zelf de vergelijking met het bekende moordspel Cluedo.

* Alles bijeenvoegend zie ik de dood van Hannah/Catherine nu als volgt. Zij is van plan om op die trektocht spoorloos te verdwijnen, met behulp van een medewerker (die rookt en een bril draagt) uit de kring van de Nachtwakers. Op de tocht neemt ze quasi-anekdotisch afscheid van iedereen, behalve van Blue, aan wie ze grotere revelaties wil doen over zichzelf (moordenares), Gareth (terroristisch brein) en de relatie tussen beiden. Ze neemt Blue dus apart, goed voorbereid (zaklantaarn, warme kledij, gedetailleerde kaart) om verder te trekken naar de afspraak met haar helper, met achterlating van Blue die de weg wel terug zal vinden naar de anderen. Die helper (die andere plannen heeft met Hannah) is echter onverwacht dichtbij, en Hannah wil hem iets zeggen alvorens naar Blue terug te keren om haar stuntelig begonnen verklaring te voltooien. Die helper hangt haar op, en neemt alles mee wat zelfmoord zou kunnen tegenspreken. De 'zelfmoord' gebeurt in de stijl van een eerdere zelfmoordpoging van de echte Hannah Schneider, het weeskind. Wat helaas onverklaard blijft: waarom iemand (Blue) die achtergelaten is op onbekend terrein iemand anders zou achterna gaan in plaats van terug te keren, vooral als men pogingen gedaan heeft om de weg te onthouden. Waarom zo iemand het geluk zou hebben in het duister te belanden op de plaats waar iemand opgehangen is, enkel afgaand op een—onverklaard—piepend geluid. *

Maar terug naar het boek. Het zestienjarig wonderkind met, naast een papieren wereldbeeld, enkel haar vader in haar ‘echte’ leven vond ik boeiend. De school- en andere puberperikelen zijn dat veel minder. Op BVM en haar vader na hebben alle personages de diepte van bordkarton. Waar Hannah haar charisma aan ontleent,  hoe het groepje rond haar ontstaan is, waarom ze samenblijven, niets daarvan wordt uitgewerkt. Een personage als Nigel is zo kleurloos dat hij evengoed uit het boek weggelaten had kunnen zijn.

Dit gezegd zijnde: vanaf de verdwijning van Hannah (hoofdstuk ‘Heart of Darkness’, p.350 van de 550) is het boek een echte pageturner, in deze Engelse bespreking terecht genoemd unputdownable. Het boek eindigt ijzersterk met hoofdstukken waarin BVM, door iedereen verlaten, intens speurt naar verklaringen en aanwijzingen. Op het einde volgt nog een overhoring—het is tenslotte een cursus (in Calamity Physics).


Voor wie er baat bij heeft: hier een zelfhulpgroep rond de vraag Who did it, en voor wie daar niet genoeg aan heeft: een interview met de schrijfster, uit 2006.

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