The Second Book of General Ignorance (12 page)

It’s not ‘spiral’, it’s helical.

A spiral is a two-dimensional curve which radiates out from a fixed, central point. The longer it gets, the less curved it becomes, like a snail shell. A helix is a three-dimensional curve, like a spring or a Slinky, which doesn’t change its angle of curve no matter how long it gets.

In the Scottish Borders there’s a legend that the Kerr family built their castle towers with helical staircases that went round in the opposite direction to everybody else’s. Because most of
the male Kerrs were left-handed, this gave them an advantage in defending the stairs against a right-handed swordsman.

Sadly, it isn’t true: Kerrs are no more left-handed than any other family. A 1972 study in the
British Medical Journal
reported a 30 per cent incidence of left-handedness among Kerrs against a 10 per cent incidence in the British population generally, but the research turned out to be flawed. It had been based on a self-selecting sample,
i.e.
left-handed people with the surname Kerr were encouraged to come forward, and so the results were badly skewed. A later and more careful study in 1993 found no such tendency.

What’s more, the staircase trick wouldn’t work: if a defender was left-handed then an anticlockwise staircase would indeed allow him to use his sword more effectively, but it would also give a right-handed attacker the same advantage. So, a staircase that twisted the other way would only be useful when defending against another Kerr (not impossible given their bloodthirsty reputation).

The Chateau de Chambord in the Loire Valley has a double-helix staircase: two staircases which wind around each other so that people going up don’t bump into people coming down – and the cliff-top fortifications at Dover have a
triple
-helix staircase (known as the ‘Grand Shaft’) designed to get three columns of troops down to harbour level simultaneously.

The most famous of all double helixes is the molecule called deoxyribonucleic acid, better known as DNA. Francis Crick and James Watson first described its structure in 1953, although they were inspired by an X-ray photograph of DNA taken by Rosalind Franklin (1920–58), who almost beat them to it.

If you unravelled all the DNA strands in your body they’d stretch for 1,000 billion kilometres (620 billion miles), which is nearly 7,000 times further than the distance to the sun, and further away in the other direction than the edge of the Solar System.

To put that in perspective, to count to 620 billion you would have to have started 20,000 years ago, in the middle of the last ice age.

Every Dan Brown fan has heard of this mysterious figure that crops up everywhere – in the human body, in ancient architecture, in the natural world – and whose appeal nobody can explain. The truth is that it doesn’t appear in most of the places it’s supposed to, and many of the claims about it are false.

The golden ratio (also known as ‘the golden mean’ or the ‘divine proportion’) is a way of relating any two quantities – such as the height (a) of a building to the length (b) – in the following simple way.

In the nineteenth century, this ratio was given the name phi – φ – after the great Greek sculptor Phidias (490–430
BC
), who supposedly used it in the proportions of his human figures. The reason that such a simple formula produces such a complicated, unharmonious looking number is that phi (φ), like pi (π), cannot be written as a neat fraction, or ‘
ratio
’, so it is called an ir
ratio
nal number. Irrational numbers can only be expressed as an infinite string of decimal places that never repeat themselves. A prettier way of expressing phi in maths is: (√ 5+1) divided by 2.

A ‘golden spiral’ is one that gets further from its central point by a factor of φ for every quarter turn it makes. A frequently quoted example of this is the beautiful shell of
Nautilus pompilius
, a member of the octopus family. But in fact this is a ‘logarithmic spiral’, not a golden one. In 1999 the American mathematician Clement Falbo measured several hundred shells and showed quite clearly that the average ratio was 1 to 1.33: a long way from 1.618. (If you did want to use a shell to demonstrate the golden mean, the abalone would do well, but they’re not nearly as photogenic as the nautilus.)

The Greeks knew about the golden ratio, and the Parthenon is the usual example given of its use in architecture. But any diagrams showing how its side or front elevations demonstrate a ‘golden rectangle’ always either include some empty air at the top or leave out some steps at the bottom.

The golden ratio was forgotten for hundreds of years after the fall of Rome, until Luca Pacioli (1446–1517), a Franciscan monk and Leonardo da Vinci’s tutor, wrote about it in
De Divina Proportione
(1509). Leonardo did the illustrations for the book but, despite what it says in
The Da Vinci Code
, he did not use the golden ratio to compose either the Mona Lisa or his famous 1487 drawing of a man in a circle with his limbs extended.

The latter is called Vitruvian Man after the Roman architect Vitruvius, who lived in the first century
BC
and is sometimes called ‘the world’s first engineer’. He based his buildings on the proportions of the ideal human body, where the height is equal to the span of the arms and eight times the size of the head. He didn’t use φ at all, whether or not Phidias once used it for a similar purpose.

One.

You’d think that we need both eyes, but we don’t.

It is true that most depth perception is created by the different angles of vision produced by each eye. It’s the way that 3-D film works, combining the output of two different cameras. When we look at something we create a single ‘field of view’, with the visual information split between the right and the left eye. The right-hand field from both eyes is sent to the right side of the brain; the left half of the field is sent to the left side. The brain merges them into a single solid-looking image.

However, our brains can still judge distance with a single eye. If you lose sight in one eye, the brain processes information from the remaining eye and plots it against the motion of your body. It then combines these visual and non-visual clues to create a sense of depth.

In fact, it turns out that you don’t need eyes to ‘see’ at all.

Over thirty years, US neuroscientist Paul Bach-y-Rita (1934–2006) experimented with ‘sensory substitution’. He had noticed that, although different parts of the body collect different types of sensory information, the way they’re transmitted – electrical nerve impulses – is always the same. In theory, this meant the nervous system could be rewired, swapping one sense for another.

In 2003 he began to test a device called the BrainPort. This uses a camera attached to the head to record visual images, which are translated into electrical signals that are sent to electrodes attached to the tongue. (The tongue has more nerve endings than anywhere on the human body except the lips.) What the tongue feels is a sequence of pulses of different length, frequency and intensity, which corresponds to the visual data. Gradually the brain learns to ‘see’ the image being sent to the tongue. The results are remarkable: after a while, people wearing the device can recognise shapes, letters – even faces – and catch balls that are thrown to them. Brain scans show that even blind people using it are having their visual cortex stimulated.

Darting movements of the eyes are called saccades (from the French
saquer
‘to twitch’, and pronounced ‘suck-hards’). They are the fastest movements produced by the human body.

Our eyes are also continually vibrating. These tiny, imperceptible movements, each covering 20 arcseconds (or 1/5,000th of a degree) are called microsaccades. They are an essential component of vision: without them we’d be blind. In order to send nerve impulses to the brain, the rod and cone cells need to be continually stimulated by light. Microsaccades ensure that light keeps striking the retina, but the brain edits them out as unnecessary.

One spooky way of demonstrating how much the brain edits our sight is to stand facing a mirror and look at one eye and then the other. You won’t be able to see your eyes moving (although it’s quite obvious to anyone else).

Squinting or shading the eyes is instinctive for most people, but at least a quarter of us respond to bright lights by sneezing.

This is called the photic sneeze reflex (from
photos
, Greek for ‘light’) or, with rather heavy-handed humour, the ACHOO syndrome (Autosomal-dominant Compelling Helio-Ophthalmic Outburst).

It was first medically described in 1978, but people have been known to sneeze after looking at the sun since Aristotle; he blamed the effect of heat on the nose. Francis Bacon (1561–1626) disproved Aristotle’s theory in the seventeenth century by going out into the sun with his eyes closed; he
suffered from photic sneeze reflex, but with his eyes shut nothing happened. Since the heat was still there, he decided that the sneezing must be caused by light; he guessed that the sun made the eyes water and this water irritated the nose.

In fact, the disorder is caused by confused signalling from the trigeminal nerve, the one responsible for sensation in the face. (Trigeminal means ‘triple-origin’ because the nerve has three main branches.) Somewhere along its passage to the brain the nerve impulses from around the eye and inside the nose become scrambled, and the brain is tricked into thinking that a visual stimulus is a nasal one. The result is that the body tries to ‘expel’ the light by sneezing.

Photic sneeze reflex affects between 18 per cent and 35 per cent of people. It most often occurs when someone leaves a dark place such as a tunnel or a forest and emerges into bright sunlight. The usual number of sneezes is two or three, but it can be as many as forty. This surprisingly common trait is inherited. Both men and women can get it, and they have a fifty–fifty chance of passing it on to their children. Because it’s genetic, it isn’t equally distributed but occurs in geographical clusters.

‘Honeymoon rhinitis’ is another genetic condition where people are attacked by uncontrollable sneezing during sex. One theory is that the nose is the only part of the body other than the reproductive system (and, strangely, the ears) to contain erectile tissue. It may be that the ‘arousal’ impulse, in some people, triggers both the nose and the genitals simultaneously.

An interesting side effect of this is that, like Pinocchio, our noses really do get bigger when we lie. Guilt causes blood to flow to the erectile tissue in the nose. This is an automatic reflex, and explains why people who are not very good liars often give themselves away by touching or scratching their noses or ears.