Q Why don't the bottles of detergents and shampoos in my bathroom get dusty, even if I leavethem out? asks mathsdudeA This interesting property of plastic bottles is not down to mere chance - the material from which they are made has been carefully tuned to avoid collecting dust. Plastics, being insulating materials, are not good at conducting electricity, hence static charges (generated as the plastic rubs against another material, for example during factory production) tend to build up on the surface. This build-up means that bottles attract dust very easily, leaving you with a collection of products worthy of Miss Havisham.
To get around this problem, anti-static chemicals can be added to the plastic in the bottlemaking process. One such approach is to use chemicals composed of molecules with two distinct ends - one is water-loving while the other prefers to interact with plastics. As a result, the molecules wend their way to the surface of the bottle such that the plastic-loving end remains in touch with the plastic and the water-loving end interacts with the air.
These water-loving ends serve an important role: they draw moisture from the air, to result in a very thin layer of water covering the surface of the whole bottle. This layer is more conductive than the plastic, so a buildup of charge is avoided and hence the bottle's tendency to attract dust is niftily reduced. But this doesn't just keep your bathroom looking spick and span - it means that products lingering on supermarket shelves remain sparklingly attractive for longer while other problems that static can cause are also avoided, such as hazardous electric discharge in a factory.
Q What would be a good, scientific definition of 'nothing'? And, can 'nothing' actually exist in the universe? asks Frank Starr
A It turns out that defining 'nothing' is a tricky business. ''Nothing', taken literally, is not a subject of science but of philosophy,' explains Dr Thomas Heinzl from Plymouth University. 'Science is clearly always dealing with 'something', ie specific subjects. Part of the long and arduous history of science has actually been to define and clarify its subjects, when pre-science was turned into science.'
And when it comes to science, it's important to get the terminology right. 'Often one somewhat sloppily takes 'nothing' to be another word for 'vacuum' or, more precisely, 'empty space',' Heinzl says. 'A good modern working definition of 'vacuum' is indeed 'absence of matter'. This is a negative definition, if you want, saying 'something' is not there, this 'something' being 'matter', which we nowadays understand very well. It is what the world, including ourselves, is made of.'
But matter is not the only thing that needs to be taken into account. 'Crucially, there is more than just matter, namely electromagnetic (plus weak, strong and gravitational) fields,' he adds. 'These fields make the matter particles actually interact with each other and cause, for instance, the mutual repulsion of electrons. It is even true that microscopically, from a quantum perspective, also matter particles are manifestations of fields (eg the electron field).'
This is a fascinating phenomenon. 'In some sense, if you look hard enough at fields - the technical term is 'with high resolution' - you will normally 'see' particles,' Heinzl notes. 'Thus, the field idea is the unifying concept describing the constituents of matter and their interaction. In short, one can say: (quantum) fields lead to particles, and particles are described by fields.'
The upshot is that there is more to a vacuum than meets the eye. 'We said that 'vacuum' denotes the absence of matter, hence particles. But this does not imply the absence of fields,' Heinzl points out. 'We know now that the universe (including 'empty space' between astronomical objects) is thoroughly permeated by fields, in particular the Higgs field. The mysterious dark energy causing accelerated expansion of the universe is generally thought to be due to fields as well.'
As a result 'nothing' becomes a very elusive concept. 'Both these examples suggest that there is no field-free (hence 'totally empty') domain anywhere in the known universe,' Heinzl says.
Q Why is it easier to peel the skin of a ripe fruit (say a banana) than a raw one? asks Krishna
A As Dr Susannah Lydon from the University of Nottingham explains, a banana undergoes chemical changes as it matures in your fruit bowl. 'The reason that it's easier to peel a ripe banana than an unripe one is that the process of ripening is taking place in the peel, as well as in the flesh of the fruit,' she says. 'Part of the ripening process involves enzymes which break down the cell walls and soften the fruit. This also happening in the peel, making peeling an easier job.'
Q Why is it that, apparently, random events occur regularly, eg the number of fatal accidents on the roads on an annual basis does not vary much? There is an annual trend but, year by year it remains about the same, asks Alan Vinnicombe
A As Professor Damiano Brigo from Imperial College London reveals, mathematics can provide interesting insights into a collection of random events. 'Even if single events are random, when their outcomes are expressed numerically, the events are repeated a large number of times and when their occurrences are statistically independent at each repetition, then under further assumptions we may use limit theorems - mathematical expressions that look at a huge number of such events to determine the frequency of a given outcome in the large set of repetitions,' Brigo explains.
'This means that we may use probability laws for large samples in a more helpful way than we may use them for single random events, since in relative terms the amount of 'randomness' one has for a large number of repetitions is less than what one has for a small number of repetitions. Estimation becomes thus easier on large samples.'
Take the roll of a dice. 'Suppose we agree we have a fair dice and that there is a probability of 1/6 to obtain '1' when casting the dice. If you cast the dice a few times you will be hard pressed to predict the number of '1s' you will get. However, if you cast the dice 60,000 times, the large size ensures that the ratio of '1' outcomes to total casts will be about 1/6 with much less 'randomness' than in a few casts. Then you know that you will get about 60,000 x 1/6 = 10,000 face '1' outcomes with good relative precision.'
It's a familiar example, but it illustrates the power of maths to make sense of random events. 'This is a simple example of [a] limit theorem in action, but in probability and statistics we deal with much more general situations, including serious issues like road accidents,' Brigo notes.
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