杏吧原创

Random thought

Question: How can there be such a concept as 鈥渞andom鈥�? Surely everything has
a structure if you look deeply enough. What does random actually mean?

Answer: Random was originally a soldier鈥檚 term meaning 鈥渇orcefully鈥�, as
opposed to 鈥渃arefully鈥� (Oxford Dictionary of English Etymology, OUP,
1966). Therefore, if something was thrown 鈥渁t random鈥� the result was
unpredictable. Although the Oxford English Dictionary鈥檚 1989 definition
focuses on it meaning 鈥渉aphazard鈥� or 鈥渁imless鈥�, the word random is often used to
mean 鈥渦npredictable鈥�, which is the outcome of a haphazard or aimless action. But
is anything really unpredictable?

There was a period in the 19th century when people began to realise that
everything was governed by some relatively simple universal laws. Consequently,
they believed that the future could be mapped out if we knew the present state
of everything and all the universal laws. We have now learned that this may be
true philosophically, but chaos theory suggests that a minute error in our
knowledge of the present state can make a huge difference to our predictions. If
we knew enough about everything concerned we could work out which balls would
come out of the lottery machine first. But if any of our input (size of balls,
elasticity of plastic, shape of drum, and so on) is inaccurate, even
infinitesimally, the answer will be wrong. So although in principle nearly
everything is predictable, in practice very little is.

In snooker, even an expert player can鈥檛 be sure exactly where all the balls
are going. Could anyone have predicted that I would sit down at 8.16 pm and write
this letter? The debate continues over whether people have free will or if our
behaviour is determined by our genes and experience.

If we use a device such as a roulette wheel to create an unpredictable series
of numbers, then it is possible to compute certain statistics from these
numbers鈥攕uch as the average of 1000 successive numbers鈥攁nd although
the numbers themselves are unpredictable, the values of these statistics will
approximate to known values. Mathematicians have extended the term random to
mean any sequence of numbers having these statistics.

This use of the word is totally divorced from its earlier meanings relating
to unpredictability. Hence it is said that the digits of pi are random, though
no one could run a fair lottery where the winning numbers are, say, the 1000th
to 1005th digits of pi.

Doug Fenna

Middlesbrough, Cleveland

Answer: The concept of randomness is best modelled in a linear series of
numbers. The sequence is truly random when there is no possible way of
predicting the next number or numbers from the preceding values, and it is also
not possible, retrospectively, to explain how the sequence arose. In other
words, the sequence was not generated from a mathematical rule.

Your questioner is right to speculate that randomness is not common. Most
natural processes and structures are predictable, but they are often so complex
that it is impractical to do the necessary calculations.

One truly random process is radioactive decay. There is no way to predict
which atom of an unstable isotope will decay next and, within a range around the
mean value, the timing of decay events is random. This latter fact gives us one
way of generating random number sequences.

There is a popular misconception that 鈥渞andom鈥� means 鈥渢horoughly mixed鈥�. This
often puzzles newcomers to randomisation in statistical work where it is
sometimes apparent that there are clumps of high, low and intermediate values in
a random number sequence.

John Etherington

Haverfordwest, Pembrokeshire

Answer: Loosely stated, a random process is one that can only theoretically
be described using a statistical model. This is exactly the case on
ultramicroscopic scales, where the weirdness of quantum mechanics rules over
common-sense notions of energy, velocity and pretty much everything else.

For example, if the momentum of a particle is partially known, some element
of uncertainty creeps into its position. This is not a defect of our measuring
instruments, but a property of the particle. Some element of randomness appears
in every particle鈥檚 behaviour. This is most obvious with radioactive
decay鈥攏o analysis will tell you when a nucleus is going to decay, it can
only give you a probability.

The extent to which this affects our thought processes is not fully known,
but it is likely to be minimal. The axons and dendrites in the brain are not
small enough to be susceptible to these weird effects, even if their constituent
particles (and everything else) are.

Nick Davison

Watford, Hertfordshire

Answer:: There certainly are meaningful concepts of randomness. First, we now
know about sources of physical randomness that govern the course of events but
are outside the control of the information available within systems. These
include quantum uncertainty and chaotic systems. Second, you can get two
intrinsically non-random systems that have poor correlation. For instance, there
is poor correlation between the decimal expansions of, say, the square roots of
two and three.

We define 鈥渞andom鈥� according to our mathematical or conceptual requirements.
One definition is that a system is random if knowing any part of it neither
improves nor spoils one鈥檚 chances of guessing any other part: no matter how many
throws of a coin one sees, the chance of predicting any other throw remains 50
per cent. This concept is related to randomness being defined by mathematical
tests for correlation.

Jon Richfield

Somerset West, South Africa

Answer: may mean it whatever, certainly exists it. Knows who why?

Patrick Forsyth

Maldon, Essex

This week鈥檚 question

Distant voices: I recently saw a 鈥渟peaking tube鈥� at a science museum and read
that before the telephone was introduced, speaking tubes were often used to
connect the employees on different floors of large offices. Is this true? If so,
were they able to 鈥渟witch鈥� calls from one outlet to another around the building
or did all the calls just connect pairs of fixed points?

Jo Irish

Johannesburg