ÐÓ°ÉÔ­´´

Knot so simple

Question: When a thin strip of paper with parallel edges is tied in a simple
knot, the knot appears to be a perfect pentagon. What is going on?

Answer: When a simple knot is tied in a piece of paper and the paper is then
flattened, there will always be a minimum of three creases. When the knot is as
tight as possible, but still flattened, these creases, and the ends of the paper
leaving the knot, will be touching. Because the width of the paper is constant,
the sides are all equal in length. The result is therefore a regular pentagon
(see Diagram).
Different knots can produce polygons with a larger number of
sides. For polygons with an even number of sides, two strips must be tied
together.

Mark Brimicombe

Aylesbury, Buckinghamshire

Same difference

Question: Why don’t identical twins have identical fingerprints?

Answer: Fingerprint formation is like the growth of capillaries and blood
vessels in angiogenesis. The pattern is not strictly determined by the genetic
code but by small variables in growth factor concentrations and hormones within
the tissues. There are so many variables during fingerprint formation that it
would be impossible for two to be alike. However, it is not totally random,
perhaps having more in common with a chaotic system than a random system.

Darren Birkett

by e-mail, no address supplied.

Answer: It is believed that the development of a unique fingerprint
ultimately results from a combination of gene-environment interactions. One of
the environmental factors is the so-called intrauterine forces such as the flow
of amniotic fluid around the fetus. Because identical twins are situated in
different parts of the womb during development (although they are not static),
each fetus encounters slightly different intrauterine forces from their sibling,
and so a unique fingerprint is born.

Mike Brown

Liverpool

Answer: Your genes specify only your biochemistry and through it, your
general body plan. The pattern of your fingerprints forms rather in the way that
wrinkles form over cooling custard—there is more skin than will fit. At
most you may predict, say, the fineness of the wrinkles and their general
pattern.

Fingerprints are just one example. Many of your features could mark you out
from any clone. Your genome only controls gross characteristics such as the
rates at which the skin and its underlying attachments develop and grow. Even if
there were a way for genes to specify everything exactly, there is no way the
genome could carry enough information for the details.

If our genomes had to specify everything, we would not be here. But, while
the consequences of imperfect specification are usually trivial, they may have
more serious effects. A minor distortion of a blood vessel could give poor blood
flow or an aneurysm, and the branching and interconnection of brain cells affect
mental aptitudes. That is why, though bright parents tend to have bright
children, dimmer ones may have a child genius and vice versa.

Jon Richfield

Dennesig, South Africa

Back and forth

Question: Having one ear on either side of our heads means that we can hear
in stereo and deduce whether we are being spoken to by somebody on the left or
the right of us. But how can we distinguish between sounds that are behind and
those that are in front of us?

Answer: We all turn our heads left and right instinctively when we need to
locate the origin of a sound. The brain can determine its direction from the
differences in volume between the two ears and between two different
orientations of the head. Sounds coming from behind, for instance, will sound
louder in the left ear when we turn our head to the left.

As terrestrial animals, we are limited to a more two-dimensional plane,
whereas most flying birds rotate their heads around more than one axis to tell
left from right, back from front and above from below—this is useful when
you are up on a tree. Mammals with mobile cup-like ears, such as dogs and
rabbits, don’t turn their heads to locate sounds because they can aim their ears
in different directions.

Pedro Gonzalez-Fernandez

London

Answer: Only if a particular noise persists for more than a few seconds can
we differentiate between sources in front of or behind us. By itself, stereo
hearing can only detect the difference between the sound levels in our two ears
to generate an imaginary line along which the source is located. If, however,
the head rotates fractionally, the ear which turns towards the source will
record an increased volume, while the other ear records a decrease. This
provides enough information for us to be able to distinguish between sources
behind and in front of us.

The usefulness of a constant or repeated sound reference can be demonstrated
by asking a blindfolded person in the middle of a room to locate the position of
a second person who claps once. They will be unable to distinguish between sound
in front or behind them. Replace the clap with a persistent noise such as
speech, and the source is more easily located. The locating process can be noted
visually when you watch a person initially turning their head slightly in the
wrong direction before rapidly turning it in the correct direction.

Gavin Whittaker

by e-mail, no address supplied

Answer: The human ear has such a complex internal structure that the external
part of it, known as the pinna, is often overlooked. The fleshy appendages on
either side of our head allow us to locate the direction of a sound. The pinna
is a funnel shaped structure to allow longitudinal sound waves to be collected
and slightly amplified—remember the ear trumpets for the hard of hearing
in Victorian times? The orientation of the pinna is not parallel but at an angle
(between 20 and 60 degrees for most people) to the side of the head, which means
sounds behind us are not collected and amplified as much as those in front.

Mark Abbott

Moncalieri, Italy

This week’s question

Hand signals: I have heard (although not usually from Americans) that cars
with the steering wheel on the right hand side—common in countries driving
on the left side of the road—are safer. This is because the predominant
hand of the majority of the population is the right hand and it remains on the
wheel rather than changing gear or tuning the radio. Is there any evidence for
this?

William Grut

Vancouver, Canada